Answer
$0, \frac{\pi}{2}, \pi, \frac{3\pi}{2}$
Work Step by Step
Step 1. $tan(2\theta)=0 \longrightarrow 2\theta=k\pi \longrightarrow \theta=\frac{k\pi}{2}$
Step 2. Within $[0,2\pi)$, we have $\theta=0, \frac{\pi}{2}, \pi, \frac{3\pi}{2}$
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