Which identity to use?

Geometry Level 5

\[\large F=\displaystyle\sum_{r=0}^{\infty}\left((-1)^r\dfrac{\cos^3 3^r}{3^r}\right)\]

If \(F\) can be written in the form \(\dfrac ab\cos^c d\), where \(a,b,c\) and \(d\) are positive integers with \(a,b\) coprime, find \(a+b+c+d\).

Clarification: All angles are measured in radians.

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