# How do you simplify sin^-1 (sin ((2pi)/3))?

The inverse sine is multivalued, so we need to include $\frac{2 \pi}{3} ,$ its supplement which shares a sine, and all coterminal angles:
$\arcsin \sin \left(\frac{2 \pi}{3}\right) = \frac{2 \pi}{3} + 2 \pi k \mathmr{and} \frac{\pi}{3} + 2 \pi k \quad$ integer $k$
The principal value is $\frac{\pi}{3}$