\textbf{107-} Suppose $A$ is the solution set of the trigonometric equation $\left(1+\cos(2\alpha)\right)\!\left(1+\cos(4\alpha)\right)\!\left(1+\cos(8\alpha)\right) = \dfrac{1}{8}$, in the interval $[0, \pi]$. What is the maximum element of $A$?
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(1) $\dfrac{5}{7}\pi$ \hfill (2) $\dfrac{6}{7}\pi$ \hfill (3) $\dfrac{7}{9}\pi$ \hfill (4) $\dfrac{8}{9}\pi$
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