Answer
$\{\frac{\pi}{4},\pi,\frac{5\pi}{4} \}$
Work Step by Step
Step 1. The equation gives two solutions: $tan(x)=1$ and $cos(x)=-1$
Step 2. For $tan(x)=1$, we have the reference angle as $x=\frac{\pi}{4}$ and we can find all x-values in $[0,2\pi)$ as $x=\frac{\pi}{4},\frac{5\pi}{4}$
Step 3. For $cos(x)=-1$, we can find all x-values in $[0,2\pi)$ as $x=\pi$
Step 4. The solutions for the original equation in $[0,2\pi)$ are $\{\frac{\pi}{4},\pi,\frac{5\pi}{4} \}$
