If `x gt y gt z gt 0`, then find the value of `"cot"^(-1) (xy + 1)/(x - y) + cot^(-1).(yz + 1)/(y - z) + cot^(-1).(zx + 1)/(z - x)`

Explanation

To solve the problem, we need to find the value of the expression:

\[ \cot^{-1}\left(\frac{xy + 1}{x - y}\right) + \cot^{-1}\left(\frac{yz + 1}{y - z}\right) + \cot^{-1}\left(\frac{zx + 1}{z - x}\right) \]

### Step-by-Step Solution:

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