Let $\omega = {e^{{{i\pi } \over 3}}}$, and a, b, c, x, y, z be non-zero complex numbers such that $a + b + c = xa + b\omega + c{\omega ^2} = ya + b{\omega ^2} + c\omega = z$ Then the value of $${{{{\left| x \right|}^2} + {{\left| y \right|}^2} + {{\left| z \right|}^2}} \over {{{\left| a \right|}^2} + {{\left| b \right|}^2} + {{\left| c \right|}^2}}}$$ is