Solve: `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 will follow these steps:

### Step 1: Rewrite \( \cot^{-1} x \)
We know that:
\[ \cot^{-1} x = \frac{\pi}{2} - \tan^{-1} x \]
Using this identity, we can rewrite the equation:
...