Prove that: \[ \left(3 \cos \frac{\pi}{3} \sec \frac{\pi}{3}-4 \sin \frac{5 \pi}{6} \tan \frac{\...

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Prove that:
\[
\left(3 \cos \frac{\pi}{3} \sec \frac{\pi}{3}-4 \sin \frac{5 \pi}{6} \tan \frac{\pi}{4}\right) \cos 2 \pi=1 \text {. }
\]
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