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 \(a+b+c\).