A complex cosine

Geometry Level 5

\[ \large \dfrac { \cos { \left( \dfrac { \pi }{ 504 } \right) } +\cos { \left( \dfrac { \pi }{ 1008 } \right) } }{ \cos { \left( \dfrac { \pi }{ 672 } \right) } } = x + \dfrac1x \]

Let \(x\) a complex number different from zero satisfying the equation above. The option that correctly express the value of \({ x }^{ 2016 }\) is...

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