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

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