Prove that: \[ \frac{\sin 5 A-\sin 7 A+\sin 8 A-\sin 4 A}{\cos 4 A+\cos 7 A-\cos 5 A-\cos 8 A}=\...

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Prove that:
\[
\frac{\sin 5 A-\sin 7 A+\sin 8 A-\sin 4 A}{\cos 4 A+\cos 7 A-\cos 5 A-\cos 8 A}=\cot 6 A
\]
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