Odd Powers Only

Algebra Level 4

\[ \large \sum_{m=0}^{2015} \left( x^{2m+1} + \dfrac1{x^{2m+1}} \right)^2 \]

If \(x\) is a complex number such that it satisfies the constraint \( \left( x + \frac1x\right)^2 = 2\), find the value of the summation above.

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