inverse sin is arcsin.
From definition arcsin function:
[tex]\arcsin x=y \qquad \Rightarrow \qquad \sin y = x \\ \hbox{Here you've got} \ \ \sin x \ \ \hbox{instead} \ \ x, \ \ \hbox{so:} \\ \sin x = \sin y \qquad \Rightarrow \qquad x=y+2k\pi \qquad \Rightarrow \qqyad y=x+2k \pi \\ \\ \hbox{So your equation is:} \\ \boxed{x=\frac{1}{6}+2k\pi } \\ \\ \hbox{Everywhere} \ \ k\in\mathbb{C}[/tex]