We know that the domain and range of the principal value branch of function $\mathit{s}\mathit{i}{\mathit{n}}^{-1}$ is defined as:
$\mathit{s}\mathit{i}{\mathit{n}}^{-1}$ " [- 1 , 1] → $\left[-\frac{\mathit{\pi }}{2},\frac{\mathit{\pi }}{2}\right]$
∴ sin $\left[\frac{\mathit{\pi }}{3}-\mathit{s}\mathit{i}{\mathit{n}}^{-1}\left(-\frac{1}{2}\right)\right]$ = sin $\left[\frac{\mathit{\pi }}{3}-\left(-\frac{\mathit{\pi }}{6}\right)\right]$
= sin $\left[\frac{\mathit{\pi }}{3}+\frac{\mathit{\pi }}{6}\right]$
= sin $\left[\frac{\mathit{\pi }}{2}\right]$
= 1