Easier than it looks

Algebra Level 3

kScos(2kπ11)\sum_{k \in S} \cos\left(\frac{2k\pi}{11}\right)

Find the value of the summation above where S={1,2,3,5,7,11}S = \{ 1,2,3,5,7,11 \} : all the prime numbers between 2 and 11, together with 1.

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