Find all non-zero real numbers x, y, z which satisfy the system of equations:
(x^2 + xy + y^2)(y^2 + yz + z^2)(z^2 + zx + x^2) = xyz,
(x^4 + x^2y^2 + y^4)(y^4 + y^2z^2 + z^4)(z^4 + z^2x^2 + x^4) = x^3y^3z^3.