Write the value of `tan^(-1){2sin(2cos^(-1)(sqrt(3))/2)}dot`

Explanation

To solve the problem \( \tan^{-1}\left(2\sin\left(2\cos^{-1}\left(\frac{\sqrt{3}}{2}\right)\right)\right) \), we will follow these steps:

### Step 1: Find \( \cos^{-1}\left(\frac{\sqrt{3}}{2}\right) \)

The value of \( \cos^{-1}\left(\frac{\sqrt{3}}{2}\right) \) corresponds to the angle whose cosine is \( \frac{\sqrt{3}}{2} \). This angle is \( \frac{\pi}{6} \) radians.

\[
\cos^{-1}\left(\frac{\sqrt{3}}{2}\right) = \frac{\pi}{6}
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