Answer
$\{0, \frac{\pi}{3}, \frac{5\pi}{3} \}$
Work Step by Step
Step 1. Let $u=cos(x)$, we have
$2u^2-3u+1=0$ or $(2u-1)(u-1)=0$
Step 2. For $u=1$ or $cos(x)=1$, we have $x=0$
Step 3. For $u=\frac{1}{2}$ or $cos(x)=\frac{1}{2}$, we have $x=\frac{\pi}{3}, \frac{5\pi}{3}$
Step 4. We have the solution set as $\{0, \frac{\pi}{3}, \frac{5\pi}{3} \}$
