If \( \mathrm{A}+\mathrm{B}+\mathrm{C}=\pi \), find the value of : ...

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If \( \mathrm{A}+\mathrm{B}+\mathrm{C}=\pi \), find the value of :
\[
\left|\begin{array}{ccc}
\sin (A+B+C) & \sin B & \cos C \\
-\sin B & 0 & \tan A \\
\cos (A+B) & -\tan A & 0
\end{array}\right|
\]
\( \mathrm{P} \)
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