Cryptic Cotangent Products

Geometry Level 5

\[\large X = \prod_{k=1}^{3015} \cot\left[\dfrac{\pi}{3}\left(1-\dfrac{3^k}{3^{3015} - 1}\right)\right] \]

and

\[\large Y = \prod_{k=1}^{3015} \cot\left[\dfrac{\pi}{3}\left(\dfrac{1}{2}-\dfrac{3^k}{3^{3015} - 1}\right)\right] \]

Evaluate \(\left(\dfrac{2X}{Y}\right)^4\)

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