The value of `sin^(-1)("cot"(sin^(-1)((2-sqrt(3))/4+cos^(-1)(sqrt(12))/4+sec^(-1)sqrt(2))))i s` (a)`0` (b) `pi/2` (c) `pi/3` (d) none of these

Explanation

To solve the problem step by step, we need to simplify the expression given in the question:

**Given Expression:**
\[ \sin^{-1}\left(\cot\left(\sin^{-1}\left(\frac{2 - \sqrt{3}}{4}\right) + \cos^{-1}\left(\frac{\sqrt{12}}{4}\right) + \sec^{-1}\left(\sqrt{2}\right)\right)\right) \]

### Step 1: Calculate \(\sin^{-1}\left(\frac{2 - \sqrt{3}}{4}\right)\)
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