Answer
$\frac{\pi}{4},\frac{\pi}{2},\frac{3\pi}{4}, \frac{3\pi}{2}$
Work Step by Step
Step 1. $2sin(\theta)cos(\theta))=\sqrt 2cos(\theta) $.
Thus $cos(\theta)=0$ or $sin(\theta)=\frac{\sqrt 2}{2}$
Step 2. For $sin(\theta)=\frac{\sqrt 2}{2}$, we have $\theta=2k\pi+\frac{\pi}{4}$ and $\theta=2k\pi+\frac{3\pi}{4}$
Step 3. For $cos(\theta)=0$, we have $\theta=2k\pi+\frac{\pi}{2}$ and $\theta=2k\pi+\frac{3\pi}{2}$
Step 4. Within $[0,2\pi)$, we have $\theta=\frac{\pi}{4},\frac{\pi}{2},\frac{3\pi}{4}, \frac{3\pi}{2}$