Minimario's trigonometric expression

Algebra Level 3

\[ (\cos 12^\circ) \times (\cos 24^\circ) \times (\cos 48^\circ) \times ( \cos96^\circ) = - \frac{a}{b}, \]

where \(a\) and \(b\) are positive coprime integers. What is the value of \( a+b \)?

This problem is posed by Minimario M.

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