Left column: probability density function P(λ|Ψ,  i_o) of the 2D projected angle (λ) obtained from the distribution of Ψ_star, BH at z = 0.18. We also use a spline function to describe the obtained PDF. In the lower left panel, we show the different distributions obtained through spline function description for different values of i_o (every 10°). Right column: we generated the plots using the same statistics but without specifying the sense of the BH vector to maintain consistency with observations.