Question: When was Prince Frederick William Of Solms-Braunfels's wife born?

Context paragraphs:
title: Amalia of Solms-Braunfels
paragraph_text: Amalia of Solms- Braunfels( 31 August 1602, Braunfels – 8 September 1675, The Hague), was Princess consort of Orange by marriage to Frederick Henry, Prince of Orange. She acted as the political adviser of her spouse during his reign, and acted as his de facto deputy and regent during his infirmity from 1640 – 47. She also served as chair of the regency council during the minority of her grandson William III, Prince of Orange from 1650 until 1672. She was the daughter of count John Albert I of Solms- Braunfels and countess Agnes of Sayn- Wittgenstein.
title: Ferdinand, Prince of Solms-Braunfels
paragraph_text: Ferdinand Wilhelm Ernst, 2nd Prince of Solms- Braunfels( 8 February 1721 in Braunfels – 2 October 1783, ibid.) was the second Prince of Solms- Braunfels. He was the son of Frederick William, Prince of Solms- Braunfels( 1696 – 1761) by his first wife Princess Magdalena Henrietta of Nassau- Weilburg( 1691 – 1725).
title: Alexander Frederick, Landgrave of Hesse
paragraph_text: Alexander Frederick, Landgrave of Hesse( 25 January 1863, Copenhagen – 26 March 1945) was a Hessian Prince. He was the son of Prince Frederick William of Hesse- Kassel and Princess Anna of Prussia. From 1888–1925 he was Head of the House of Hesse, but abdicated his position to his brother Prince Frederick Charles of Hesse. He was visually handicapped from birth, and this, in addition to his morganatic marriage, played a part in his decision to abdicate.
title: Christine Charlotte of Solms-Braunfels
paragraph_text: Christine Charlotte of Solms- Braunfels( 10 November 1690 in Greifenstein – 16 October 1771 in Homburg) was a Countess of Solms- Braunfels by birth and by marriage Landgravine of Hesse- Homburg.
title: Frederick William, Prince of Solms-Braunfels
paragraph_text: Prince Frederick William of Solms- Braunfels( 11 January 1696 in Braunfels – 24 February 1761, Braunfels) was the first Prince of Solms- Braunfels. He was the son of Count William Maurice of Solms- Braunfels( 1651 – 1724) and his wife Magdalene Sophie of Hesse- Homburg( 1660 – 1720), a daughter of William Christoph, Landgrave of Hesse- Homburg, and his first wife.
title: William, Prince of Solms-Braunfels
paragraph_text: Wilhelm Christian Karl, 3rd Prince of Solms Braunfels (9 January 1759, in Braunfels – 20 March 1837, in Braunfels) was by succession an immediate Prince, then a nobleman and head of the Princely House of Solms-Braunfels, a Prussian major general and Hessian deputy.
title: Prince Frederick William of Solms-Braunfels
paragraph_text: Prince Frederick William of Solms- Braunfels( 22 October 1770 in Braunfels – 13 April 1814 in Slawentzitz) was a Prussian Major General. He was the fourth son of Ferdinand William Ernest, 2nd Prince of Solms- Braunfels( 1721 – 1783) and Countess Sophie Christine Wilhelmine of Solms- Laubach( 1741 – 1772). He became known mainly through his marriage to Princess Frederica of Mecklenburg- Strelitz. She was the widow of Prince Louis Charles of Prussia( 1773 – 1796). When she became pregnant in 1798, he married her in order to avoid a scandal. The daughter died soon after birth. Frederick William was alleged to have been strongly inclined to consume alcohol and had to quit military service in 1805 for health reasons. He also lost his income and even his brother advised Frederica to divorce. She was initially against it, but when in 1813, she met Ernest Augustus, King of Hanover( 1771 – 1851), she, too, wanted the divorce. Before they got around to it, however, Frederick William died, in 1814 in Sławięcice.
title: Frederica of Mecklenburg-Strelitz
paragraph_text: Frederica of Mecklenburg-Strelitz ("Friederike Louise Caroline Sophie Charlotte Alexandrine") (3 March 1778 – 29 June 1841) was a German princess who became, by marriage, princess of Prussia, princess of Solms-Braunfels, Duchess of Cumberland in Britain and Queen of Hanover (in Germany) as the consort of Ernest Augustus, King of Hanover (the fifth son and eighth child of King George III). She was born in the "Altes Palais" of Hanover as the fifth daughter of Charles II, Duke of Mecklenburg-Strelitz, and his first wife, Frederica, daughter of Prince George William of Hesse-Darmstadt. Her father assumed the title of Grand Duke of Mecklenburg on 18 June 1815. Duchess Frederica was the niece of her future mother-in-law, Queen Charlotte, through her father.
title: Countess Amalie Henriette of Solms-Baruth
paragraph_text: Countess Amalie Henriette Charlotte of Solms-Baruth (Kliczków, 30 January 1768 – Karlsruhe, 31 October 1847) was a countess by birth of Solms-Baruth. She was the only child of John Christian II, Count of Solms-Baruth and his wife, Friederike Louise of Reuss-Köstritz.
title: Johannetta of Sayn-Wittgenstein (1561–1622)
paragraph_text: Johanetta of Sayn-Wittgenstein (15 February 1561 – 13 April 1622) was a daughter of Count Louis I of Sayn-Wittgenstein and his first wife, Anna of Solms-Braunfels, who was a relative of Amalia of Solms-Braunfels.

Reasoning steps:
Prince Frederick William of Solms-Braunfels spouse Frederica of Mecklenburg-Strelitz
Frederica of Mecklenburg-Strelitz date of birth 3 March 1778

Answer: spans: 3 March 1778