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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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