240 Followers Problem - 1

Geometry Level 3

$\large \cos \theta _{1} + \cos \theta _{2} + \cos \theta_{3}$

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.