Sorry, I'm not sure if my question is clear then. I already found the solutions: $z= \frac{1}{e^{\frac{2\pi i}{7}}-1}, \frac{1}{e^{\frac{4\pi i}{7}}-1}, \frac{1}{e^{\frac{6\pi i}{7}}-1}, \frac{1}{e^{\frac{8\pi i}{7}}-1}, \frac{1}{e^{\frac{10\pi i}{7}}-1}, \frac{1}{e^{\frac{12\pi i}{7}}-1}$ I am struggling to find how to prove all of those solutions have the same real part and what that real part is. This equation is a 7th root of unity so there has to be some "trick"
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