Prove that: \[ 3 \cos ^{2} \frac{\pi}{4}+\sec \frac{2 \pi}{3}+5 \tan ^{2} \frac{\pi}{3}=\frac{29...

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Prove that:
\[
3 \cos ^{2} \frac{\pi}{4}+\sec \frac{2 \pi}{3}+5 \tan ^{2} \frac{\pi}{3}=\frac{29}{2}
\]
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