Let $\omega=\mathrm{e}^{\mathrm{i} \mathrm{x} / 3}$, and $\mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{x}, \mathrm{y}, \mathrm{z}$ be non-zero complex numbers such that $$ \begin{aligned} & a+b+c=x \\ & a+b \omega+c \omega^2=y \\ & a+b \omega^2+c \omega=z \end{aligned} $$ Then the value of $\frac{|x|^2+|y|^2+|z|^2}{|a|^2+|b|^2+|c|^2}$ is