Distributions of θ and cos(4θ) for all subhaloes in the box. Top panel: distribution of the values of the angle between the spin of the subhaloes and the direction of the closest filament (θ). Bottom panel: distribution of values of cos(4θ) for all the subhaloes in the box. In both panels, the solid lines show the measured distribution of values of θ and cos(4θ) (green: j_tot, blue: j_gas, red: j_stars, and purple: j_{gas + stars}). The dashed black lines show the expected distribution for a random population of subhaloes (Eq. (3), top panel, and Eq. (4), bottom panel).