The value of is equal to

MATHEMATICS · Single correct · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

The value of ∑k=1131sin⁡(π4+(k−1)π6)sin⁡(π4+kπ6)\sum_{k=1}^{13} \frac{1}{\sin \left( \frac{\pi}{4} + \frac{(k-1)\pi}{6} \right) \sin \left( \frac{\pi}{4} + \frac{k\pi}{6} \right)} is equal to (1) 3−33 - \sqrt{3} (2) 2(3−3)2(3 - \sqrt{3}) (3) 2(3−1)2(\sqrt{3} - 1) (4) 2(2+3)2(2 + \sqrt{3})

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