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 $a+b+c$ .