Threatening Trigonometry

Geometry Level 4

cos4π7+cos43π7+cos45π7\cos^{ 4} \dfrac{\pi}{7} + \cos^{4} \dfrac{ 3 \pi}{7} + \cos^{4} \dfrac{5 \pi}{7}

If the above expression is equals to ab \dfrac {a}{b} where aa and bb are coprime positive.

Find a+ba+b.

Image Credit: Wikimedia Heptagon by SoluS
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