Equations in inverse functions

Solve $\sin^{-1}x = \frac{2\pi}{3}$. Taking the sine of both sides gives $x = \sin\frac{2\pi}{3} = \frac{\sqrt{3}}{2}$. But $\sin^{-1}\frac{\sqrt{3}}{2} = \frac{\pi}{3}$, not $\frac{2\pi}{3}$. What went wrong?