Question 596137
Using the identity 


2*sin(x)*cos(x) = sin(2x)


we get


<img src="http://latex.codecogs.com/png.latex?\LARGE 2\sin\left(\frac{2\pi}{11}\right)\cos\left(\frac{2\pi}{11}\right) = \sin\left(2\times\frac{2\pi}{11}\right) = \sin\left(\frac{4\pi}{11}\right)" title="x" />


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So 
<img src="http://latex.codecogs.com/png.latex?\LARGE 2\sin\left(\frac{2\pi}{11}\right)\cos\left(\frac{2\pi}{11}\right)=\sin\left(\frac{4\pi}{11}\right)" title="x" />


which means you are 100% correct. Nice job.