\[\large \left(x + \frac{1}{x}\right)^2 + \left(x^2 + \frac{1}{x^2}\right)^2 + \left(x^3 + \frac{1}{x^3}\right)^2 + \cdots + \left(x^{2016} + \frac{1}{x^{2016}}\right)^2\]

If \({ x }^{ 2 }+x+1=0\), evaluate the expression above.

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