Answer
$0$
Work Step by Step
Suppose $\theta =\cos (2 \pi)$
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 $[0,\pi]$ .
But the value $ a=2 \pi $ does not lie in the range of $[0, \pi]$.
Therefore, we have $ \cos^{-1}[\cos (2 \pi)]=0$
