Looks like you have some kind of non-deciduous live oaks there...deciduous ones work better because their leaves are thinner, let more light through...however, you can open it up a little with some judicious 'shotgun pruning'. Just aim a 12ga at the sun and open up a nice ragged hole...kinda extreme but it works. Your yield won't be as good as full sun but plenty of people grow under trees successfully...good luck!