where the proof is provided in the Supplemental Material. The above focused initial conditions only affect angles {θ j } for j ∈ {1, • • • , N -1}, whereas the {ϕ j } angles are sampled randomly in the range [0, 2π]. This effectively evaluates the integrals over {θ j }, but leaves the original integrals over {ϕ j }. From Eq. 74, we further derive the expression of the angles {θ n } as follows