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$\sqrt{2+\sqrt{2+2 \cos 4 \theta}}=$
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The correct answer is:
$2 \cos \theta$
$\begin{aligned} \sqrt{2+\sqrt{2+2 \cos 4 \theta}} &=\sqrt{2+\sqrt{2(1+\cos 4 \theta)}} \\ &=\sqrt{2+\sqrt{2 \times 2 \cos ^{2} 2 \theta}}=\sqrt{2+2 \cos ^{2} 2 \theta} \\ &=\sqrt{2\left(1+\cos ^{2} 2 \theta\right)}=\sqrt{2 \times 2 \cos ^{2} \theta}=2 \cos \theta \end{aligned}$
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