$a=2\left(\sin(2x)\right)^{4}+\cos(4x)$

$x=\frac{-\arccos(3-4a)+2\pi n_{1}+\pi }{8}\text{, }n_{1}\in \mathrm{Z}$
$x=\frac{\arccos(3-4a)+2\pi n_{2}-\pi }{8}\text{, }n_{2}\in \mathrm{Z}\text{, }a\geq \frac{1}{2}\text{ and }a\leq 1$