If tan^{-1}x+tan^{-1}y+tan^{-1}z=pie, prove x+y+z=xyz

TAN-1X + TAN-1Y + TAN-1Z = PIE

TAN-1 ( X + Y / 1- XY) + TAN-1Z = PIE { TAN-1X + TAN-1Y = TAN-1 ( X + Y / 1- XY) }

TAN-1 ( X + Y / 1-XY) + Z = PIE

1- Z[(X + Y) /(1-XY)]

(X + Y / 1 - XY) + Z = TAN(PIE)

1- Z[(X + Y) /(1-XY)]

(X + Y / 1 - XY) + Z = 0

1- Z[(X + Y) /(1-XY)]

[(X + Y) / (1 - XY)] + Z = 0

(X + Y) / (1 - XY) = -Z

X + Y = -Z(1 - XY)

X + Y = -Z + XYZ

X + Y + Z = XYZ