Evaluation of an interesting Integral – mathoverflow.net

Supposedly the answer is 1 but I have no idea how to evaluate this thing analytically. $$f(n) = \frac{2}{\pi} \int_{0}^{\infty} 2\cos(x) \cdot \frac{\sin(x)}{x} \cdot \frac{\sin(x/3)}{x/3} \cdot \...

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