If \( z^{2}+z+1=0 \), where \( z \) is a complex number, the value ...

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If \( z^{2}+z+1=0 \), where \( z \) is a complex number, the value of \( \left(z+\frac{1}{z}\right)^{2}+\left(z^{2}+\frac{1}{z^{2}}\right)^{2}+\left(z^{3}+\frac{1}{z^{3}}\right)^{2}+\ldots+\left(z^{6}+\frac{1}{z^{6}}\right)^{2} \)
\( \mathrm{P} \) is
[AIEEE 2006, 6M]
(a) 18
(b) 54
(c) 6
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