Solve: `sin[2\ cos^(-1){cot(2\ tan^(-1)x)}]=0`

Explanation

To solve the equation \( \sin[2 \cos^{-1}(\cot(2 \tan^{-1}(x)))] = 0 \), we can follow these steps:

### Step 1: Understand the sine function
The sine function equals zero at integer multiples of \( \pi \):
\[ \sin(\theta) = 0 \implies \theta = n\pi, \quad n \in \mathbb{Z} \]
Thus, we can set:
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