Answer
$\{ \frac{\pi}{2}, \frac{3\pi}{4}, \frac{7\pi}{4} \}$
Work Step by Step
Step 1. The equation gives two solutions $tan(x)=-1$ and $sin(x)=1$
Step 2. For $tan(x)=-1$, we can find all x-values in $[0,2\pi)$ as $x=\frac{3\pi}{4}, \frac{7\pi}{4}$
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 $\{ \frac{\pi}{2}, \frac{3\pi}{4}, \frac{7\pi}{4} \}$
