The number of elements in the set \( S=\left\{\theta \in[-4 \pi, 4 \pi]: 3 \cos ^{2} 2 \theta+6 ...

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The number of elements in the set \( S=\left\{\theta \in[-4 \pi, 4 \pi]: 3 \cos ^{2} 2 \theta+6 \cos 2 \theta-10 \cos ^{2} \theta+5=0\right. \) is
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