Solve for `x :` `tan^(-1)x+2cot^(-1)x=(2pi)/3`

Explanation

To solve the equation \( \tan^{-1} x + 2 \cot^{-1} x = \frac{2\pi}{3} \), we can follow these steps:

### Step 1: Use the identity for cotangent
We know that:
\[ \tan^{-1} x + \cot^{-1} x = \frac{\pi}{2} \]
From this, we can express \( \cot^{-1} x \) in terms of \( \tan^{-1} x \):
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