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

Explanation

`cot^(-1)(x y+1)/(x-y)+cot^(-1)(y z+1)/(z y-z)+cot^(-1)(z x+1)/(z-x)`


`=>tan^(−1)(x−y​)/((1−xy))+tan^(−1)((y−z​)/(1+yz))+tan^(−1)((z−x​)/(1+zx))`


`=tan^(−1)x−tan^(−1)y+tan^(−1)y−tan^(−1)z+tan^(−1)z+tan^(−1)x`


`=0`