There are integers v, w, x, y, z and real numbers 0 \leq \theta<\theta^{\prime} \leq \pi such that
\cos 3 \theta=\cos 3 \theta^{\prime}=v^{-1}, \quad w+x \cos \theta+y \cos 2 \theta=z \cos \theta^{\prime}
Given that z \neq 0 and v is positive, find the sum of the 4 smallest possible values of v.