Answer
$\theta=4k\pi+\frac{8\pi}{3}$ or $4k\pi+\frac{10\pi}{3}$ (k is an integer),
$\theta=\frac{8\pi}{3}, \frac{10\pi}{3},\frac{20\pi}{3}, \frac{22\pi}{3},\frac{32\pi}{3}, \frac{34\pi}{3}$.
Work Step by Step
$sin(\frac{\theta}{2})=-\frac{\sqrt 3}{2}$,
$\frac{\theta}{2}=2k\pi+\frac{4\pi}{3}$ or $2k\pi+\frac{5\pi}{3}$,
$\theta=4k\pi+\frac{8\pi}{3}$ or $4k\pi+\frac{10\pi}{3}$ (k is an integer),
Six examples: $\theta=\frac{8\pi}{3}, \frac{10\pi}{3},\frac{20\pi}{3}, \frac{22\pi}{3},\frac{32\pi}{3}, \frac{34\pi}{3}$.
