Only Two Terms Remains, Which Terms?

Geometry Level 5

\[ \large f(x) = \sum_{n=1}^{\infty}{\sin \left(\dfrac{2x}{3^n}\right) \sin \left( \dfrac{x}{3^n}\right)} \]

Find the value of \( \left( f\left( \dfrac \pi 3\right) \right)^{-1} \).

Bonus: Can you determine \( f(x) \) in closed form?

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