Secular evolution of the obliquities of TOI-1710 from four-body secular integrations. The semimajor axis of the intermediate companion varies across panels. The obliquity evolution of TOI-1710 A b (red) and the hypothetical intermediate companion X (blue) are shown. The companion mass is fixed at 9 M_J, and the initial mutual inclination with the M dwarf is i_XB = 55°. The green region marks the 2σ constraints on the obliquity of the observed planet, with the fraction of time spent within this region indicated by f_obs. Panels (a) and (c) remain within the allowed window for much less time than panel (b). In all cases, the eccentricity of planet b remains nearly the same as the initial value.