Only Two Terms Remains, Which Terms?

Geometry Level 5

f(x)=n=1sin(2x3n)sin(x3n) \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 (f(π3))1 \left( f\left( \dfrac \pi 3\right) \right)^{-1} .

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

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