Uroš III's decision not to attack the Byzantines after the victory at the Battle of Velbazhd against Bulgaria resulted in the alienation of many nobles, who sought to expand to the south. By January or February 1331, Dušan was quarreling with his father, perhaps pressured by the nobility. According to contemporary pro-Dušan sources, evil advisors turned Uroš III against his son; he decided to seize and exclude Dušan of his inheritance. Uroš III sent an army into Zeta against his son, the army ravaged Skadar, but Dušan had crossed the Bojana. A brief period of anarchy in parts of Serbia took place before the father and son concluded peace in April 1331. Three months later, Uroš III ordered Dušan to meet him. Dušan feared for his life and his advisors persuaded him to resist, so Dušan marched from Skadar to Nerodimlje, where he besieged his father. Uroš III fled, and Dušan captured the treasury and family. He then pursued his father, catching up with him at Petrić. On 21 August 1331, Uroš III surrendered, and on the advice or insistence of Dušan's advisors, he was imprisoned. Dušan was crowned King of All Serbian and Maritime lands in the first week of September. The civil war had prevented Serbia from aiding Ivan Stephen and Anna Neda in Bulgaria, who were deposed in March 1331, taking refuge in the mountains. Ivan Alexander of Bulgaria feared for the danger of Serbia as the situation there had settled, and immediately sought peace with Dušan. As Dušan wanted to move against richer Byzantium, the two made peace and an alliance in December 1331, accepting Ivan Alexander as ruler. It was sealed with the marriage of Dušan and Helena, the sister of Ivan Alexander.
Question: How many months after Dušan was crowned king was the peace alliance made between him and Byzantium?
Answer: 3