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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