You probably shouldn't. Trees compete with turf for light, water, and nutrients. Trees and turf also have very different water requirements; trees require infrequent deep waterings, while turfgrasses need frequent, shallow waterings. Trees planted in turf often develop unusually shallow root systems in an effort to maximize their water intake from irrigation. This often results in trees that are susceptible to wind-throw and all the subsequent structural damage that can cause. For these reasons, growing turf under large trees is always difficult and is not recommended. Instead of fighting a losing battle, you might consider removing the turf from the dripline inward, mulching the area, and installing ornamental plants adapted to heavy shade, or planting a shade-loving ground cover.
