Drop it

Geometry Level 4

\[ \large \prod_{k=1}^n \left( 1 + 2\cos\dfrac{2\pi\cdot 3^k}{3^n + 1} \right) \]

Evaluate the product above, where \(n\) denote a positive integer.

If you think the product above has no unique value, submit your answer as \(-100\).

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