Bizarre cosines of gp!

Geometry Level 4

$\large \left(1+\cos^{2}20^{\circ}\right) \left(1+\cos^{2}40^{\circ}\right) \left(1+\cos^{2}80^{\circ}\right)$

If the value of the expression above can be represented in the form $$\dfrac{a}{b}$$. for coprime positive integers $$a$$ and $$b$$, find the value of $$a+b$$.

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