Answer
$\dfrac{2\pi}{3}$
Work Step by Step
Suppose $\theta =\cos (\dfrac{4\pi}{3})$
This gives: $\cos^{-1} \theta=\cos^{-1}[\cos (\dfrac{4\pi}{3})]$
The inverse property states that $\cos^{-1}(\cos a)=a $ satisfies for every $ a $ in the range $[0,\pi]$ .
Therefore, we have $ \cos^{-1}[\cos (\dfrac{4\pi}{3})]=\dfrac{2\pi}{3}$
