If \( A+B+C=180^{\circ}, \frac{\sin 2 A+\sin 2 B+\sin 2 C}{\sin A+\sin B+\sin C}=k \sin \frac{A}...

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If \( A+B+C=180^{\circ}, \frac{\sin 2 A+\sin 2 B+\sin 2 C}{\sin A+\sin B+\sin C}=k \sin \frac{A}{2} \) \( \sin \frac{B}{2} \sin \frac{C}{2} \) then the value of \( 3 k^{3}+2 k^{2}+k+1 \) is equal to
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