Sin^2(x/2)=3cos^2(x/2)

[latex]sin^2\frac{x}{2}-3cos^2\frac{x}{2}=0\\\\sin^2\frac{x}{2}-3(1-sin^2\frac{x}{2})=0\\\\4sin^2\frac{x}{2}-3=0\\\\sin^2\frac{x}{2}=\frac{3}{4}\\\\\frac{1-cosx}{2}=\frac{3}{4}\\\\1-cosx=\frac{3}{2}\\\\cosx=-\frac{1}{2}\\\\x=\pm(\pi -\frac{\pi}{3})+2\pi n,n\in Z[/latex] [latex]x=\pm \frac{2\pi }{3}+2\pi n[/latex]