# Trigonometric Identity Maybe?

Geometry Level 4

I made an elementary trigonometric identity complicated to get this expression.

$\LARGE \displaystyle\sum_{k=1}^{10} \left ( \sin \left ( \frac {2\pi k}{11 } \right ) - i \cos \left ( \frac {2\pi k}{11 } \right ) \right )$

What is the value of $$4$$ times the square of the said expression?

Details and Assumptions:

• $$i$$ denote the imaginary number: $$i^2 = -1$$

Also see this.

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