tan-1x+tan-1y+tan-1z = π/2
=) tan-1x+tan-1y = π/2-tan-1z
=) tan(tan-1x+tan-1y) = tan(π/2-tan-1z)
= ) x+y/1-xy = cot(tan-1z) [since tan(A+B)=tanA+tanB/1-tanAtanB & tan(π/2-A)=cotA]
=) x+y/1-xy = cot(cot-11/z) [since tan-1A=cot-11/A]
= ) x+y/1-xy = 1/z
=) xz+yz=1-xy [by cross multiplication]
=) xy+yz+zx=1
AS DESIRED //