8.010. $8 \cos z \cos \left(60^{\circ}-z\right) \cos \left(60^{\circ}+z\right)+1=0$.
## Solution.

We have

$4 \cos z\left(\cos 2 z+\cos 120^{\circ}\right)+1=0, \quad 4 \cos z \cos 2 z-2 \cos z+1=0 \Leftrightarrow$ $\Leftrightarrow 2 \cos z+2 \cos 3 z-2 \cos z+1=0, \quad \cos 3 z=-\frac{1}{2}, \quad 3 z= \pm \frac{2}{3} \pi+2 \pi k$, $z= \pm \frac{2}{9} \pi+\frac{2 \pi k}{3}, k \in Z$.

Answer: $z= \pm \frac{2}{9} \pi+\frac{2 \pi k}{3}, k \in Z$.