Do this without calculator

Geometry Level 4

\[\dfrac{\sqrt{16\cos\left(\dfrac{2\pi}{7}\right)+8\cos\left(\dfrac{4\pi}{7}\right)+x}}{2}=\sin\left(\dfrac{2\pi}{7}\right)+\sin\left(\dfrac{4\pi}{7}\right)+\sin\left(\dfrac{6\pi}{7}\right)\]

Solve the equation above for \(x\).

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