Trigonometric Identity Maybe?

Geometry Level 4

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

k=110(sin(2πk11)icos(2πk11))\large \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 expression above?

Details and Assumptions: i=1i =\sqrt {-1} denotes the imaginary unit.

Also try this.


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