If  a>b>c>0,then cot−1ab+1a−b+cot−1bc+1b−c+cot−1ca−1c−a

Given a>b>c>0.  Now cot-1ab+1a-b+cot-1bc+1b-c+cot-1ca+1c-a=cot-1ab+1a-b+cot-1bc+1b-c+cot-1-ac+1a-c                                                                                      =cot-1a-cot-1b+cot-1b-cot-1c+π-cot-1a-cot-1c                                                                                             ∵if x>y, then cot-1xy+1x-y=cot-1x-cot-1y,  also cot-1-x=π-cot-1x                                                                                      =π