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∣eae2a(e3a−1)ebe2b(e3b−1)ece2c(e3c−1)∣ \left | \begin{array}{ccc} e^a & e^{2a} & (e^{3a}-1) \\ e^b & e^{2b} & (e^{3b}-1) \\ e^c & e^{2c} & (e^{3c}-1) \\ \end{array} \right | ∣∣∣∣∣∣eaebece2ae2be2c(e3a−1)(e3b−1)(e3c−1)∣∣∣∣∣∣
if a,ba,ba,b and ccc are cube roots of unity, find the determinant of the matrix above.
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