If `A, B, C` are three angles of a triangle, then prove that $ \begin{vmatrix} \sin\ (A+B+C) & \sin\ (A+C) & \cos\ C \\ -\sin\ B & 0 & \tan\ A \\ \cos\ (A+B) & \tan\ (B+C) & 0 \end{vmatrix} = 0 $