Q.Let $z_{1}, z_{2}$and$z_{3}$ be three complex numbers on the circle$|z| = 1$ with $\arg(z_{1}) = -\pi/4, \arg(z_{2}) = 0$and $\arg(z_{3}) = \pi/4. If |z_{1} \bar{z}_{2} + z_{2} \bar{z}_{3} + z_{3} \bar{z}_{1}|^{2} = \alpha + \beta \sqrt{2}, \alpha, \beta \in \mathbb{Z},$ then the value of $\alpha^{2} + \beta^{2}$ is: