# Not Quite the Unity I'm Looking For

Algebra Level 4

$\displaystyle \dfrac{1}{12} \sum_{n=1}^{24} \left ( z^{n} + \dfrac{1}{z^{n}} \right )^{2}$

What is the value of the expression above if we are given that $$z^{2} - z + 1 = 0$$?

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