$$\cos^{2}n-\cos\ x+\frac{1}{4}=0$$
$\left\{\begin{matrix}x=\arccos(\frac{4\left(\cos(n)\right)^{2}+1}{4})+2\pi n_{1}\text{, }n_{1}\in \mathrm{Z}\text{, }&\exists n_{2}\in \mathrm{Z}\text{ : }\left(n\geq \pi n_{2}+\frac{\pi }{6}\text{ and }n\leq \pi n_{2}+\frac{5\pi }{6}\right)\\x=-\arccos(\frac{4\left(\cos(n)\right)^{2}+1}{4})+2\pi n_{2}\text{, }n_{2}\in \mathrm{Z}\text{, }\exists n_{2}\in \mathrm{Z}\text{ : }\left(n\geq \pi n_{2}+\frac{7\pi }{6}\text{ and }n\leq \pi n_{2}+\frac{11\pi }{6}\right)\text{, }&\exists n_{2}\in \mathrm{Z}\text{ : }\left(n\geq \pi n_{2}+\frac{7\pi }{6}\text{ and }n\leq \pi n_{2}+\frac{11\pi }{6}\right)\end{matrix}\right.$