Find the exact value of the following. Draw a picture to help explain your answer.

sin^(-1)(sin(4π/3))

This is what I did:

sin^(-1)(sin(4π/3)) = sin^(-1)(-√3/2) = -π/3

Is this correct? I'm still not clear on how to determine which quadrant it should be in, but I guessed it would be quadrant 4 because the sine is negative.