We can write this equation as $x^{9}=1$. The roots of this equation will be $1, \alpha, \alpha^{2}, \alpha^{3}, \alpha^{4}, \alpha^{5}, \alpha^{6}, \alpha^{7}, \alpha^{8}$, where $\alpha = \cos\left(\frac{2\pi}{9}\right) + i\sin\left(\frac{2\pi}{9}\right)$.
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