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RootReduce[(1+7^(2/3)/((-1+(3*I)*Sqrt[3])/2)^(1/3)+((7*(-1+(3*I)*Sqrt[3]))/2)^(1/3))/6 - Cos[Pi/7]]
RootReduce[(1+7^(2/3)/((-1+(3*I)*Sqrt[3])/2)^(1/3)+((7*(-1+(3*I)*Sqrt[3]))/2)^(1/3))/6 - Cos[Pi/7]]
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