Prove that \( \cos ^{3} x+\cos ^{3}\left(\frac{2 \pi}{3}+x\right)+\...

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Prove that \( \cos ^{3} x+\cos ^{3}\left(\frac{2 \pi}{3}+x\right)+\cos ^{3}\left(\frac{2 \pi}{3}-x\right)=\frac{3}{4} \cos 3 x \).
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