# Cos + Sin = ?

Geometry Level 3

$64\cos(16^\circ) \cos(8^\circ) \cos(4^\circ)\cos(2^\circ) \cos^2(1^\circ) \sin^2(1^\circ) + \cos(32^\circ) \cos(2^\circ)$

If the value of the expression above equals to $$\dfrac{\sqrt a}b$$ for positive integers $$a$$ and $$b$$ with $$b$$ square-free, find the value of $$a + b$$.

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