Answer
$\frac{\pi}{2},\frac{3\pi}{2},\frac{2\pi}{3},\frac{4\pi}{3}$
Work Step by Step
Step 1. Rewrite the equation $1-cos^2\theta-cos^2\theta=1+cos\theta\longrightarrow 2cos^2\theta+cos\theta=0$. 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 $\theta=\frac{2\pi}{3},\frac{4\pi}{3}$