Each term gives equal value?

Algebra Level 2

Given z2+z+1=0,z^2+z+1=0, find the value of

(z+1z)2+(z2+1z2)2+(z3+1z3)2++(z21+1z21)2.\left(z+\dfrac{1}{z} \right)^2+\left(z^2+\dfrac{1}{z^2}\right)^2+\left(z^3+\dfrac{1}{z^3} \right)^2+\cdots+\left(z^{21}+\dfrac{1}{z^{21}}\right)^2.

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