Best way to grow grass in high traffic area?

I live in a rental. The previous renters had a lawn in the backyard, but obviously never used it. There is a large pine tree and a large maple tree shading the yard. We have a dog and kids so there is a lot of traffic and the grass disappeared. The soil is hard packed, but does have a nice sprinkler system. Because it's a rental we cannot cut down the trees. What is your advice, besides getting rid of the kids and dog, to grow back a nice lawn?
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