# Double Trouble

Calculus Level 5

$S_n = \left(1-\tan^4\frac{\pi}{2^3}\right) \left(1-\tan^4\frac{\pi}{2^4}\right) \left(1-\tan^4\frac{\pi}{2^5}\right) \ldots \left(1-\tan\frac{\pi}{2^n}\right)$

For $$S_n$$ as defined above, evaluate $$\displaystyle30.28 \lim_{n\to\infty}\frac{\pi^3}{S_n}$$ to the nearest Integer.

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