When did Nassau the German state join the Napoleonic wars?

Nassau, a German state, joined the Napoleonic Wars in the early 19th century, aligning itself with the French during the War of the Fourth Coalition in 1806. Following the defeat of Prussia, Nassau became part of the Confederation of the Rhine, which was established by Napoleon in 1806. However, Nassau's allegiance shifted after the War of the Sixth Coalition, as it joined the opposing forces against France in 1813.