The flow in a rapidly rotating cylinder forced to precess through a nutation angle a is investigated numerically, keeping all parameters constant except a, and tuned to a triadic resonance at a = 1º. When increasing a, the flow undergoes a sequence of well- characterized bifurcations associated with triadic resonance, involving heteroclinic and homoclinic cycles, for a up to about 4º. For larger a, we identify two chaotic regimes. In the first regime, with a between about 4º and 27º, the bulk flow retains remnants of the helical structures associated with the triadic resonance, but there are strong nonlinear interactions between the various azimuthal Fourier components of the flow. For the larger a regime, large detuning effects lead to the triadic resonance dynamics being completely swamped by boundary layer eruptions. The azimuthal mean flow at large angles results in a large mean deviation from solid-body rotation and the flow is characterized by strong shear at the boundary layers with temporally chaotic eruptions.