Trigonometry Crush 8

Geometry Level 3

$\cos^8 \left( \dfrac\pi{12} \right) - \sin^8 \left( \dfrac\pi{12} \right)$

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

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