IMO 1985 LL BEL4

Let x, y, and z be real numbers satisfying x + y + z = xyz.

IMO 1985 LL BEL4

Origin: BEL

Problem

Let x, y, and z be real numbers satisfying x + y + z = xyz. Prove that x(1 −y2)(1 −z2) + y(1 −z2)(1 −x2) + z(1 −x2)(1 −y2) = 4xyz.