240 Followers Problem - 2

Geometry Level 4

cos2θ1+cos2θ2+cos2θ3\large \cos^2 \theta_{1} + \cos^2 \theta_{2} +\cos^2 \theta_{3}

Given that cos(θ1θ2)+cos(θ2θ3)+cos(θ3θ1)=32\cos \left( \theta_{1} -\theta_{2} \right) + \cos \left( \theta_{2} -\theta_{3} \right) + \cos \left( \theta_{3} -\theta_{1} \right) = -\dfrac{3}{2} , find the value of the expression above.

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