Answer
$\frac{\pi}{2}, \frac{3\pi}{2},\frac{2\pi}{3}, \frac{4\pi}{3}$
Work Step by Step
Step 1. Factor to get $cos\theta (2cos\theta+1)=0$. Thus $cos\theta=0$ or $cos\theta=-\frac{1}{2}$
Step 2. For $cos\theta=0$, we have $\theta=\frac{\pi}{2}, \frac{3\pi}{2}$
Step 3. For $cos\theta=-\frac{1}{2}$, we have $\theta=\frac{2\pi}{3}, \frac{4\pi}{3}$