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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