Answer
$\frac{2\pi}{3}, \frac{4\pi}{3}$
Work Step by Step
Step 1. Factor the equation $ (2cos\theta+1)(cos\theta-4)=0$. Thus $cos\theta=4$ or $cos\theta=-\frac{1}{2}$.
Step 2. For $cos\theta=-\frac{1}{2}$, we have $\theta=\frac{2\pi}{3}, \frac{4\pi}{3}$
Step 3. For $cos\theta=4$, we have $\theta=none$
