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

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