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How do I solve the equation given below for values for $\epsilon$?

$$ \sum_{j=1}^{n-1} (2{\alpha_{j}}+1) ~~ \prod_{k=1,~k\neq j}^{n-1} \bigg(({\alpha_{k}}-1){\Big((2{\alpha_{k}}+3) + {\epsilon}(2{\alpha_{k}}+1)\Big)}^{2}\bigg) = 0 $$

where $\alpha_i = \cos{\dfrac{2\pi i}{n}}$, where $n$ is an even integer and $n \geqslant 8$. ($j$ is NOT the imaginary unit).

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Is this the same as your earlier question,… ? – Gerry Myerson Nov 1 '11 at 11:38
What do you get when $n$ is 2 or 3? – GEdgar Nov 1 '11 at 12:20
@ Gerry - Yes. It's related to that problem. Need help to solve this or a method to solve this one.. – Udara Nov 1 '11 at 23:33
@ GEdgar - I haven't tried when $n$ is 2 or 3 since my problem is basically to find the behavior when $n$ is greater than or equal to 8. – Udara Nov 1 '11 at 23:34

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