Prove that: \[ \tan 4 \pi-\cos \frac{3 \pi}{2}-\sin \frac{5 \pi}{6} \cos \frac{2 \pi}{3}=\frac{1...

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Prove that:
\[
\tan 4 \pi-\cos \frac{3 \pi}{2}-\sin \frac{5 \pi}{6} \cos \frac{2 \pi}{3}=\frac{1}{4}
\]
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