Show that: \[ \sin (B-C) \cos (A-D)+\sin (C-A) \cos (B-D)+\sin (A-B) \cos (C-D)=0 \]

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Show that:
\[
\sin (B-C) \cos (A-D)+\sin (C-A) \cos (B-D)+\sin (A-B) \cos (C-D)=0
\]
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