$Co{s}^{-1}\left(Cos\text{\hspace{0.33em}}10\right)=$

Here $\theta =10$radians. clearly, it does not lies between 0 and$\pi$.  But $4\pi -10$ lies between $0$ and $\pi$. 

$\therefore$$Co{s}^{-1}\left(Cos10\right)=Co{s}^{-1}\left(Cos\left(4\pi -10\right)\right)$

                                        $=4\pi -10$