Threatening Trigonometry

Geometry Level 4

\[\cos^{ 4} \dfrac{\pi}{7} + \cos^{4} \dfrac{ 3 \pi}{7} + \cos^{4} \dfrac{5 \pi}{7} \]

If the above expression is equals to \( \dfrac {a}{b} \) where \(a\) and \(b\) are coprime positive.

Find \(a+b\).

Image Credit: Wikimedia Heptagon by SoluS
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