Trigonometry Crush 8

Geometry Level 3

cos8(π12)sin8(π12) \cos^8 \left( \dfrac\pi{12} \right) - \sin^8 \left( \dfrac\pi{12} \right)

If the value of the expression above is equal to abc \dfrac {a\sqrt b}c , where a,ba,b and cc are integers with bb square-free and a,ba,b coprime, find a+b+ca+b+c.

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