Answer
$\frac{\pi}{3}, \frac{2\pi}{3},\frac{4\pi}{3}, \frac{5\pi}{3}$
Work Step by Step
1. Given $tan^2(s)=3$, we have $tan(s)=\pm\sqrt 3$.
2. For $tan(s)=\sqrt 3$, we can find a reference angle as $s_0=tan^{-1}(\sqrt 3)=\frac{\pi}{3}$. In $[0,2\pi)$, there are two solution angles $s=\frac{\pi}{3}, \pi+\frac{\pi}{3}$ or $s=\frac{\pi}{3}, \frac{4\pi}{3}$
3. For $tan(s)=-\sqrt 3$, we can find a reference angle as $s_0=tan^{-1}(\sqrt 3)=\frac{\pi}{3}$. In $[0,2\pi)$, there are two solution angles $s=\pi-\frac{\pi}{3}, 2\pi-\frac{\pi}{3}$ or $s=\frac{2\pi}{3}, \frac{5\pi}{3}$
4. The solutions are $\frac{\pi}{3}, \frac{2\pi}{3},\frac{4\pi}{3}, \frac{5\pi}{3}$
