Answer
$\{ \frac{\pi}{2},\frac{3\pi}{2} \}$
Work Step by Step
Step 1. Factor the equation as $cot^2(x)(sin(x)-1)=0)$, which gives two solutions $cot(x)=0$ and $sin(x)=1$
Step 2. For $cot(x)=0$, we can find all x-values in $[0,2\pi)$ as $x=\frac{\pi}{2},\frac{3\pi}{2}$
Step 3. For $sin(x)=1$, we can find all x-values in $[0,2\pi)$ as $x=\frac{\pi}{2}$
Step 4. The solutions for the original equation in $[0,2\pi)$ are $\{ \frac{\pi}{2},\frac{3\pi}{2} \}$