Answer
$x=2 \displaystyle \arcsin\frac{y}{3}$
Work Step by Step
The goal is to isolate x.
Divide with 3...
$\displaystyle \frac{y}{3}=\sin\frac{x}{2}$ $\qquad$ ...use the definition of arcsin
$\displaystyle \frac{x}{2}=\arcsin\frac{y}{3}$
($\displaystyle \frac{x}{2}$ is the number from $[-\displaystyle \frac{\pi}{2}, \displaystyle \frac{\pi}{2}]$ such that $\displaystyle \sin\frac{y}{3}=\frac{x}{2}$)
(...If $\displaystyle \frac{x}{2}\in(-\frac{\pi}{2}, \displaystyle \frac{\pi}{2})$, then $x\in(-\pi, \pi)$...)
... isolate the x by multiplying with 2 ...
$x=2 \displaystyle \arcsin\frac{y}{3}$
