If $\omega \ne 1$ is a cube root of unity and $x+y+z\ne 0,$ then prove that $\left|\frac{x}{1+\omega }\frac{y}{\omega +{\omega }^2}\frac{z}{{\omega }^2+1}\frac{y}{\omega +{\omega }^2}\frac{z}{{\omega }^2+1}\frac{x}{1+\omega }\frac{zz}{{\omega }^2+1}\frac{x}{1+\omega }\frac{y}{\omega +{\omega }^2}\right|=0$ if $x=y=z$

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