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Let 1/(a1+omega) + 1/(a2+omega)+1/(a3+om...

Let `1/(a_1+omega) + 1/(a_2+omega)+1/(a_3+omega)+ … . + 1/(a_n+omega)=i`
where `a_1,a_2,a_3` …. `a_n in R` and `omega` is imaginary cube root of unity , then evaluate `sum_(r=1)^(n)(2a_r-1)/(a_r^2-a_r+1)` .

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