Question: Vaidotas was a son of what ruler of medieval Lithuania who was the Duke of Trakai?

full_context: Document 1: Dausprungas: Dausprungas (also "Dovsprunk" in Russian sources, died before 1238) was the older brother of Mindaugas, the first King of Lithuania. Dausprungas is mentioned in the peace treaty with Galicia–Volhynia in 1219 among the 21 early dukes of Lithuania as one of the five elder dukes, the other four being Živinbudas, Daujotas, Mindaugas and Viligaila (Daujotas' brother). Since Dausprungas is the only known brother of Mindaugas, Mindaugas' nephews Edivydas and Tautvilas are presumed to be his sons. If that is true, then Dausprungas is father-in-law of Daniel of Halych and he was also married to Vykintas' sister. Because it is known that Mindaugas used to kill his relatives to gain power and because Dausprungas is not mentioned in any other sources, some imply that he was killed by Mindaugas, but others rebut since his sons still ruled their lands in 1248.
Document 2: Lithuanian Civil War (1381–84): The Lithuanian Civil War of 1381–1384 was the first struggle for power between the cousins Jogaila, Grand Duke of Lithuania and later King of Poland, and Vytautas the Great. It began after Jogaila signed the Treaty of Dovydiškės with the Teutonic Knights which was aimed against his uncle Kęstutis, father of Vytautas. Kęstutis briefly seized power in the Grand Duchy, but was betrayed by adherents of Jogaila primarily from Vilnius. During negotiations for a truce Kęstutis and Vytautas were arrested and transported to the Kreva Castle. Kęstutis died there a week later but Vytautas managed to escape and then sought an alliance with the Teutonic Knights. Subsequently their joint forces raided Lithuanian lands. Eventually the cousins were reconciled as Jogaila needed internal stability in anticipation of negotiations with the Grand Duchy of Moscow and the Kingdom of Poland regarding the possible Christianization of Lithuania. The war did not settle the power struggle; it continued during the next Lithuanian Civil War (1389–1392) which was resolved by the signing of the Ostrów Agreement. After more than ten years of struggle, Vytautas finally became the Grand Duke of Lithuania and ruled the country for thirty-eight years.
Document 3: Kęstutis: Kęstutis (] ; born ca. 1297, died on 3 August or 15 August 1382 in Kreva) was a ruler of medieval Lithuania. He was the Duke of Trakai and governed the Grand Duchy of Lithuania, 1342–82, together with his brother Algirdas (until 1377), and with his nephew Jogaila (until 1381). He ruled over the Lithuanians and Ruthenians.
Document 4: Daujotas: Daujotas was one of the 5 elder Lithuanian dukes mentioned in the peace treaty with Halych-Volhynia in 1219. In the same document Vilikaila is mentioned as brother of Daujotas which suggests that Daujotas was the older or perhaps more influential brother. The brothers are not mentioned in any other sources. Tomas Baranauskas, a modern Lithuanian historian, believes that Vilikaila and Daujotas might be sons of Stekšys, a Lithuanian duke killed in 1214.
Document 5: Vytautas: Vytautas (c. 1350 – October 27, 1430), also known as Vytautas the Great (Lithuanian: "   ", Belarusian: "Вітаўт Кейстутавіч (Vitaŭt Kiejstutavič)" , Polish: "Witold Kiejstutowicz" , Rusyn: "Vitovt", Latin: "Alexander Vitoldus") from the 15th century onwards, was a ruler of the Grand Duchy of Lithuania, which chiefly encompassed the Lithuanians and Ruthenians. He was also the Prince of Hrodna (1370–1382), Prince of Lutsk (1387~1389), and the postulated king of the Hussites.
Document 6: Algirdas: Algirdas (Belarusian: Альгерд , Russian: Ольгерд , Polish: "Olgierd" ;  1296  – May 1377) was a ruler of medieval Lithuania. He ruled the Lithuanians and Ruthenians from 1345 to 1377. With the help of his brother Kęstutis (who defended the western border of the Duchy) he created an empire stretching from the present Baltic states to the Black Sea and to within fifty miles of Moscow.
Document 7: Algirdas: Algirdas (Belarusian: Альгерд , Russian: Ольгерд , Polish: "Olgierd" ;  1296  – May 1377) was a ruler of medieval Lithuania. He ruled the Lithuanians and Ruthenians from 1345 to 1377. With the help of his brother Kęstutis (who defended the western border of the Duchy) he created an empire stretching from the present Baltic states to the Black Sea and to within fifty miles of Moscow.
Document 8: Butautas: Butautas (baptized "Henryk"; died on May 7, 1380 in Prague) was a son of Kęstutis, Grand Duke of Lithuania. He attempted to depose his uncle Algirdas and usurp power in Lithuania, but failed and was forced into exile. He joined the court of the Holy Roman Emperor and even inspired a poem about conversion to Christianity. Butautas is sometimes confused with his brother Vaidotas.
Document 9: Sigismund Kęstutaitis: Sigismund Kęstutaitis (Lithuanian: "Žygimantas I Kęstutaitis" ; Polish: "Zygmunt Kiejstutowicz" ; c. 1365 – 20 March 1440) was the Grand Duke of Lithuania from 1432 to 1440. Sigismund was his baptismal name; Sigismund's pagan Lithuanian birth name is unknown. He was the son of the Grand Duke of Lithuania Kęstutis and his wife Birutė.
Document 10: Vilikaila: Vilikaila or Viligaila was one of the 5 elder Lithuanian dukes mentioned in the peace treaty with Halych-Volhynia in 1219. He is mentioned as brother of Daujotas, which leads scholars to believe he was the younger or perhaps less influential brother. The brothers are not mentioned in any other sources. Tomas Baranauskas, a modern Lithuanian historian, believes that Vilikaila and Daujotas might be sons of Stekšys, a Lithuanian duke killed in 1214.
Document 11: Duchy of Trakai: Duchy of Trakai was a subdivision of the Grand Duchy of Lithuania during the 14th and early 15th centuries. The Duke of Trakai was an important position held either by the Grand Duke of Lithuania himself or his second-in-command.
Document 12: Trakai Peninsula Castle: Trakai Peninsula Castle is one of the castles in Trakai, Lithuania. It is located on a peninsula between southern Lake Galvė and Lake Luka. Built around 1350–1377 by Kęstutis, Duke of Trakai, it was an important defensive structure protecting Trakai and Vilnius, capital of the Grand Duchy of Lithuania, against attacks of the Teutonic Knights. Much of the castle was destroyed in the 17th century. Remaining walls and towers are preserved and protected by the Trakai Historical National Park.
Document 13: Lithuanian Civil War (1389–92): The Lithuanian Civil War of 1389–92 was the second civil conflict between Jogaila, King of Poland and Grand Duke of Lithuania, and his cousin Vytautas. At issue was control of the Grand Duchy of Lithuania, then the largest state in Europe. Jogaila had been crowned King of Poland in 1386; he installed his brother Skirgaila as ruler of Lithuania. Skirgaila proved unpopular and Vytautas attempted to depose him. When his first attempt to take the capital city of Vilnius failed, Vytautas forged an alliance with the Teutonic Knights, their common enemy – just as both cousins had done during the Lithuanian Civil War between 1381 and 1384. Vytautas and the Knights unsuccessfully besieged Vilnius in 1390. Over the next two years it became clear that neither side could achieve a quick victory, and Jogaila proposed a compromise: Vytautas would become Grand Duke and Jogaila would remain Superior Duke. This proposal was formalized in the Ostrów Agreement of 1392, and Vytautas turned against the Knights. He went on to reign as Grand Duke of Lithuania for 38 years, and the cousins remained at peace.
Document 14: Daumantas of Lithuania: Daumantas or Dovmont was the Grand Duke of Lithuania in 1282–1285. Daumantas is mentioned in chronicles only once and, in absence of any other evidence, is presumed to be a short-ruled Grand Duke who inherited the title after Traidenis' death in 1281 or 1282. It is assumed that Daumantas was succeeded by Grand Duke Butegeidis. Relationships between Traidenis, Daumantas, and Butegeidis are unknown.
Document 15: Vaidotas: Vaidotas or Wojdat (fl. 1362) was a son of Kęstutis, Grand Duke of Lithuania. In reliable historical sources he is mentioned only twice: as defender of Kaunas Castle in 1362 and as ruler of Navahrudak. Due to very limited information, his life is subject to wide-ranging theories by historians.
ground_truth: Kęstutis