240 Followers Problem - 2

Geometry Level 4

\[\large \cos^2 \theta_{1} + \cos^2 \theta_{2} +\cos^2 \theta_{3} \]

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