Answer
$\theta=k\pi+\frac{\pi}{3}$ or $k\pi+\frac{2\pi}{3}$ (k is an integer),
$\theta=\frac{\pi}{3}, \frac{2\pi}{3},\frac{4\pi}{3}, \frac{5\pi}{3},\frac{7\pi}{3}, \frac{8\pi}{3}$.
Work Step by Step
$cos(2\theta)=-\frac{1}{2}$,
$2\theta=2k\pi+\frac{2\pi}{3}$ or $2k\pi+\frac{4\pi}{3}$,
$\theta=k\pi+\frac{\pi}{3}$ or $k\pi+\frac{2\pi}{3}$ (k is an integer),
Six examples: $\theta=\frac{\pi}{3}, \frac{2\pi}{3},\frac{4\pi}{3}, \frac{5\pi}{3},\frac{7\pi}{3}, \frac{8\pi}{3}$.
