Let z1, z2 and z3 be three complex numbers on the circle |z| = 1 with arg(z1) = \(\frac{-\pi}{4}\), arg(z2) = 0, arg(z3) = \(\frac{\pi}{4}\). If \(\left|Z_{1} \bar{Z}_{2}+Z_{2} \bar{Z}_{3}+Z_{3} \bar{Z}_{1}\right|^{2}\) = \(α+β \sqrt{2}, α, β \in Z\), then the value of α2 + β2 is :
1
24
2
41
3
31
4
29