Answer
$0,\frac{\pi}{3},\frac{5\pi}{3}$
Work Step by Step
Step 1. Rewrite the equation $2(1-cos^2\theta)=3-3cos\theta \longrightarrow 2cos^2\theta-3cos\theta+1=0 \longrightarrow (cos\theta-1)(2cos\theta-1)=0$. Thus $cos\theta=1$ or $cos\theta=\frac{1}{2}$
Step 2. For $cos\theta=1$, we have $\theta=0$
Step 3. For $cos\theta=\frac{1}{2}$, we have $\theta=\frac{\pi}{3},\frac{5\pi}{3}$
