Limited trigonometry

Calculus Level 5

r=1[12rtan(π/42r)] \large \sum_{r=1}^\infty \left[ \frac1{2^r} \tan\left( \frac{\pi /4}{2^r} \right) \right ]

If the series above equals to AπB+C A\pi^B + C for integers A,BA,B and CC, find the value of A×B×CA\times B\times C.

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