JEE Maths#4

Algebra Level 4

Let z1z_1, z2z_2 and z3z_3 be three points on z=1|z|=1 in the complex plane and z1+z2+z3=0z_1 + z_2 + z_3 = 0. If θ1\theta_1, θ2\theta_2 and θ3\theta_3 are the arguments of z1z_1, z2z_2 and z3z_3 respectively, find the value of

cos(θ1θ2)+cos(θ2θ3)+cos(θ3θ1)\cos(\theta_1-\theta_2) + \cos(\theta_2-\theta_3) + \cos (\theta_3 -\theta_1)

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