If $\cos^{-1} x + \cos^{-1} y + \cos^{-1} z = 3\pi$, what is $x + y + z$?

Explanation

1. 01

   Each $\cos^{-1}$ is at most $\pi$, so all three must equal $\pi$.

2. 02

   $\cos^{-1} x = \pi$ gives $x = -1$; so $x + y + z = -3$.