Trigonometric Identity Maybe?

Geometry Level 4

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

\[\large \sum_{k=1}^{10} \left ( \sin \left ( \frac {2\pi k}{11 } \right ) - i \cos \left ( \frac {2\pi k}{11 } \right ) \right ) \]

What is the value of 4 times the square of the expression above?

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

Also try this.

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