Cos 22x -1 - cosx =√3/2 -sin 22x

[latex]cos^22x-1-cosx= \frac{\sqrt3}{2}-sin^22x\\\\\underbrace {(cos^22x+sin^22x)} _{1}-1-cosx=\frac{\sqrt3}{2}\\\\cosx=-\frac{\sqrt3}{2}\\\\x=\pm arccos(-\frac{\sqrt3}{2})+2\pi n,\; n\in Z\\\\x=\pm (\pi -\frac{\pi}{6})+2\pi n=\pm \frac{5\pi}{6}+2\pi n,\; n\in Z[/latex]