Putnam 1986 B2

Prove that there are only a finite number of possibilities for the ordered triple $T=(x-y,y-z,z-x)$, where $x,y,z$ are complex numbers satisfying the simultaneous equations $$x(x-1)+2yz = y(y-1)+2zx = z(z-1)+2xy,$$ and list all such triples $T$.