Let $$\omega = e^{\frac{i \pi}{3}}$$ and a, b, c, x, y, z be non-zero complex numbers such that
$$a + b + c = x$$
$$a + b \omega + c \omega^2 = y$$
$$a + b \omega^2 + c \omega = z$$.
Ten the value of $$\frac{\mid x \mid^2 + \mid y \mid^2 + \mid z \mid^2}{\mid a \mid^2 + \mid b \mid^2 + \mid c \mid^2}$$ is