Answer
$-\frac{11\pi}{6},-\frac{7\pi}{6},-\frac{5\pi}{6},-\frac{\pi}{6},\frac{\pi}{6},\frac{5\pi}{6}$
Work Step by Step
1. Given $3tan^2(s)=1$, we have $tan(s)=\pm\frac{3}{3}$.
2. For $tan(s)=\frac{3}{3}$, we can find a reference angle as $s_0=tan^{-1}(\frac{3}{3})=\frac{\pi}{6}$. In $[-2\pi,\pi)$, there are three solution angles $s=-2\pi+\frac{\pi}{6}, -\pi+\frac{\pi}{6}, \frac{\pi}{6}$ or $s=-\frac{11\pi}{6}, -\frac{5\pi}{6}, \frac{\pi}{6}$
3. For $tan(s)=-\frac{3}{3}$, we can find a reference angle as $s_0=tan^{-1}(\frac{3}{3})=\frac{\pi}{6}$. In $[-2\pi,\pi)$, there are three solution angles $s=-\pi-\frac{\pi}{6}, -\frac{\pi}{6}, \pi-\frac{\pi}{6}$ or $s=-\frac{7\pi}{6}, -\frac{\pi}{6}, \frac{5\pi}{6}$
4. The solutions are $-\frac{11\pi}{6},-\frac{7\pi}{6},-\frac{5\pi}{6},-\frac{\pi}{6},\frac{\pi}{6},\frac{5\pi}{6}$
