I love cos 2

Geometry Level 3

cos8(π8)+cos8(3π8)+cos8(5π8)+cos8(7π8)\large\cos ^{8}\left( \frac{\pi }{8} \right) + \cos \nolimits^{8}\left( \frac{3\pi }{8} \right) + \cos \nolimits^{8}\left( \frac{5\pi }{8} \right) + \cos \nolimits^{8}\left( \frac{7\pi }{8} \right)

If the value of the expression above equals to AB \dfrac AB for coprime positive integers, find the value of ABA - B.

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