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If a > b > c >0 , prove that cot^(-1)((...

If `a > b > c >0` , prove that `cot^(-1)((a b+1)/(a-b))+cot^(-1)((b c+1)/(b-c))+cot^(-1)((c a+1)/(c-a))=pi`

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`cot^(-1) ((ab+1)/(a-b)) + cot^(-1) ((bc+1)/(b-c))+ cot^(-1) ((ca+1/(c-a))`

`=tan^(-1) ((a-b)/(1+ab))+ tan^(-1) ((b-c)/(1+bc)) +tan^(-1) ((c-a)/(1+ca))`

`=(tan^(-1) a- tan^(-1) b)+( tan^(-1)b -tan^(-1)c)+( tan^(-1)c- tan^(-1)a)`

`=0`

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