What is the value of $\sin\left(\frac{\pi}{3} - \sin^{-1}\left(-\frac{1}{2}\right)\right)$?

Explanation

1. 01

   $\sin^{-1}\left(-\frac{1}{2}\right) = -\frac{\pi}{6}$, so the angle is $\frac{\pi}{3} + \frac{\pi}{6} = \frac{\pi}{2}$.

2. 02

   $\sin \frac{\pi}{2} = 1$.