If `tan^(-1)x+tan^(-1)y=(4pi)/5,` find `cot^(-1)x+cot^(-1)ydot`

Explanation

To solve the problem, we need to find \( \cot^{-1} x + \cot^{-1} y \) given that \( \tan^{-1} x + \tan^{-1} y = \frac{4\pi}{5} \).

### Step-by-Step Solution:

1. **Use the Identity**: We know that:
\[ \tan^{-1} x + \cot^{-1} x = \frac{\pi}{2} \]
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