Basic angle $\displaystyle = \sin^{-1}(1) = \frac{\pi}{2}$

$\displaystyle \sin$ is positive in 1st + 2nd quadrants.

$\displaystyle 3x=\sin^{-1}(1)$

$\displaystyle 3x=\frac{\pi}{2}$ (repeated) , $\displaystyle \frac{5\pi}{2}$ (repeated) , $\displaystyle \frac{9\pi}{2}$ (repeated)

Dividing through by 3

$\displaystyle x=\frac{\pi}{6}$ (repeated) , $\displaystyle \frac{5\pi}{6}$ (repeated) , $\displaystyle \frac{3\pi}{2}$ (repeated)

So these are the intercepts from $\displaystyle [0,2\pi]$

My question is, how do I get the intercepts from $\displaystyle [-2\pi,0]$ ?