Answer
$\frac{4\pi}{9}, \frac{8\pi}{9}, \frac{16\pi}{9} $
Work Step by Step
Using trigonometric identities, we have
$sec(\frac{3\theta}{2})=-2 \longrightarrow cos(\frac{3\theta}{2})=-\frac{1}{2} \longrightarrow \frac{3\theta}{2}=\pi-\frac{\pi}{3}, \pi+\frac{\pi}{3}, 2\pi+\pi-\frac{\pi}{3} \longrightarrow \theta=\frac{4\pi}{9}, \frac{8\pi}{9}, \frac{16\pi}{9} $
