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The points A,B,C represent the complex n...

The points `A,B,C` represent the complex numbers `z_1,z_2,z_3` respectively on a complex plane & the angle `B & C` of the triangle `ABC` are each equal to `1/2 (pi-alpha)` . If `(z_2-z_3)^2=lambda(z_3-z_1)(z_1-z_2) sin^2( alpha/2)` then determine `lambda`.

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