The points \( A, B, C \) represent the complex numbers \( z_{1}, z_{2}, z_{3} \) respectively on...

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The points \( A, B, C \) represent the complex numbers \( z_{1}, z_{2}, z_{3} \) respectively on a complex plane and the angle \( B \) and \( C \) of the triangle \( A B C \) are each equal to \( 1 / 2(\pi-\alpha) \).
if \( \left(z_{2}-z_{3}\right)^{2}=k\left(z_{3}-z_{1}\right)\left(z_{1}-z_{2}\right) \sin ^{2} \frac{\alpha}{2} \). then value of \( k \) is
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