Answer
$ \theta=k\pi+\frac{\pi}{3}, k\pi+\frac{2\pi}{3}$.
$\frac{\pi}{3}, \frac{2\pi}{3},\frac{4\pi}{3}, \frac{5\pi}{3},\frac{7\pi}{3}, \frac{8\pi}{3}$
Work Step by Step
Using trigonometric identities, we have
$cos(2\theta)=-\frac{1}{2} \longrightarrow 2\theta=2k\pi+\frac{2\pi}{3}, 2k\pi+\frac{4\pi}{3} \longrightarrow \theta=k\pi+\frac{\pi}{3}, k\pi+\frac{2\pi}{3}$.
Six examples $\theta=\frac{\pi}{3}, \frac{2\pi}{3},\frac{4\pi}{3}, \frac{5\pi}{3},\frac{7\pi}{3}, \frac{8\pi}{3}$
