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

Explanation

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

### Step 1: Set the sine function to zero
Since \( \sin(A) = 0 \) implies \( A = n\pi \) for any integer \( n \), we can write:
\[ 2\cos^{-1}\left(\cot\left(2\tan^{-1}(x)\right)\right) = n\pi \]
For simplicity, we will consider the case when \( n = 0 \):
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