Summing cosec between 0 and pi

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My first thought was to somehow use complex numbers to solve the problem, but I have no clue how to start. Applying De Moivre's theorem gets me nowhere, because the expression only contains sin. My next thought was to use trigonometric induction, but I didn't really start with the result, so there's not much to assume. Any help appreciated.

 

[Deleted member 4993]

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My first thought was to somehow use complex numbers to solve the problem, but I have no clue how to start. Applying De Moivre's theorem gets me nowhere, because the expression only contains sin. My next thought was to use trigonometric induction, but I didn't really start with the result, so there's not much to assume. Any help appreciated.

Applying DeMoivre's theorem:

sin(Θ) = [e^jΘ - e^-jΘ]/(2j) where j = √(-1)