I am experimenting with an idealized three-body system based on the Sun-Earth-Moon system. In my system the orbits of the Moon and Earth about the Earth-Moon barycenter, and the orbits of the Earth-Moon barycenter and the Sun about the Earth-Sun barycenter, are perfect circles located in the same plane. The Earth's axis of rotation is tilted 24° from vertical. The solar year is exactly 360 days and the lunar month is exactly 30 days. There are no other planets in the system; the only things gravitationally acting on the Earth are the Sun and the Moon. The Sun and Moon are perfect spheres, while the Earth is a spheroid with a flattening (oblateness) of 1/288.

Under these conditions, how much would the Earth's axis of rotation experience precession and nutation?

My understanding is that a lot of the torque in real life comes from the fact that the real orbits are not perfect circles and are not in exactly the same plane, plus the perturbations from the other planets, so without these aspects the effects should be lessened, but I don't know by how much.