# How do you calculate tan^-1(tan((4pi)/3))?

For any trig function,$T$
${T}^{-} 1 \left(T \left(\theta\right)\right) = \theta$
Therefore ${\tan}^{-} 1 \left(\tan \left(\frac{4 \pi}{3}\right)\right) = \frac{4 \pi}{3}$