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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