Answer
$\{ \frac{\pi}{4},\frac{5\pi}{4} \}$
Work Step by Step
Step 1. The equation gives two solutions: $cot(x)=0$ and $tan(x)=1$
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 $tan(x)=1$, we can find all x-values in $[0,2\pi)$ as $x=\frac{\pi}{4},\frac{5\pi}{4}$
Step 4. We need to exclude $x=\frac{\pi}{2}, \frac{3\pi}{2}$ since they $tan(x)$ becomes undefined at these values.
Step 5. The solutions for the original equation in $[0,2\pi)$ are $\{ \frac{\pi}{4},\frac{5\pi}{4} \}$
