The principal value of cos^-1(cos(2π)/3)+sin^-1(sin(2π)/3) is:

$\cos^{-1}(\cos\frac{2π}{3})+\sin^{-1}(\sin\frac{2π}{3})$

$\frac{2π}{3}+(π-\frac{2π}{3})$  {since $\frac{2π}{3}>\frac{π}{2}$ and domain of $\sin^{-1}x$ is $x∈[-\frac{π}{2},\frac{π}{2}]$}

$=π$