# Jack Bauer is back!

Geometry Level 4

If $$\sin^{24} \left ( \frac {\pi}{24} \right ) + \cos^{24} \left ( \frac {\pi}{24} \right ) = \frac {a+b \sqrt3}{2^c }$$ for positive integers $$a,b,c$$ such that $$c$$ is minimized, what is the value of $$c+1$$?

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