The value of tan^-1≤ft[2 sin 2 cos^-1 ≤ft((√3)/2 ) ]

$\tan^{-1}\left[2 \sin \left[2 \cos^{-1} \left(\frac{\sqrt{3}}{2} \right) \right]\right]$

$=\tan^{-1} \left[2 \sin \frac{2 × \pi}{6} \right]$

$=\tan^{-1} \left[2 \sin \frac{\pi}{3} \right]$

$= \tan^{-1}\left[2 × \frac{\sqrt{3}}{2}\right]$

$= \tan^{-1}[\sqrt{3}]$

$=\frac{\pi}{3}$