# 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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