Write the value of `tan^(-1)[2sin(2cos^(-1)(sqrt(3))/2)]` .

Explanation

Let `cos^(-1)frac{sqrt 3}{2}=x`

`cos x=frac{sqrt 3}{2}`

`x=pi/6` where `x in [0, pi]`

`2cos^(-1)frac{sqrt 3}{2}=pi/3`

Then the expression reduces to `tan^(-1)(2 sin frac{pi}{3})`

`sin frac{pi}{3}=frac{sqrt 3}{2}`

`2 sin frac{pi}{3}=sqrt 3`

`tan^(-1) sqrt 3=pi/3`