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At least, Wolfram Alpha says it's wrong. Could it be right and WA is wrong?
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The cube root of e^(i17pi/6) has 3 answers, one of which is

e^(i17π/18)
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If you look at the section called "All 3rd roots of e^(5 i π/6)" on WA, it is the second of the three solutions given.
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