Sec−11+x2+Cosece−11+y2y+Cot−11z=π then

Let x=tanA, y=tanB and z=tanC.   Then sec-11+x2+cosec-11+y2y+cot-11z=π ⇒sec-11+tan2A+cosec-11+tan2BtanB+cot-11tanC=π ⇒sec-1secA+cosec-1cosecB+cot-1cotC=π ⇒A+B+C=π ⇒tanA+tanB+tanC=tanAtanBtanC ⇒x+y+z=xyz