Prove that: \[ 2 \cos ^{2} \frac{\pi}{4}+2 \sin ^{2} \frac{3 \pi}{4}+2 \sec ^{2} \frac{\pi}{3}=10 \]

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Prove that:
\[
2 \cos ^{2} \frac{\pi}{4}+2 \sin ^{2} \frac{3 \pi}{4}+2 \sec ^{2} \frac{\pi}{3}=10
\]
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