The definition and the formula in question:
The equations he refers to:
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Obtaining the formula seems straight forward but It has been quite difficult for me for some reason. My problem is with the term $$\frac{\sin^{2}\left(\frac{1}{2}nt\right)}{\sin^{2}\left(\frac{1}{2}t\right)}$$ and I get the denominator easily, but I can't get the numerator right and I checked my steps for errors multiple times.