If `x > y > z >0,` then find the value of `cot^(-1)((x y+1)/(x-y))+cot^(-1)((y z+1)/( y-z))+cot^(-1)((z x+1)/(z-x))`

Explanation

To solve the problem, we need to evaluate the expression:

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

Given that \(x > y > z > 0\).

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