Let \( w=e^{i \pi / 3} \), where \( i=\sqrt{-1} \) and \( a, b, c, ...

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Let \( w=e^{i \pi / 3} \), where \( i=\sqrt{-1} \) and \( a, b, c, x, y \) and \( z \) be non-zero complex numbers such that
W
\[
\begin{array}{c}
a+b+c=x \\
a+b w+c w^{2}=y \\
a+b w^{2}+c w=z .
\end{array}
\]
The value of \( \frac{|x|^{2}+|y|^{2}+|z|^{2}}{|a|^{2}+|b|^{2}+|c|^{2}} \), is
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