# 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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