Answer: Grass is a plant that prefers ample sun, good, rich, humousy soil, and a steady supply of moisture to grow well. Often, a large tree will make it difficult to grow grass beneath it due to its blocking the light and rain with its canopy and the root system taking moisture and nutrients from the soil. Once grass fails to thrive, nature will try to fill the gap -- in this case moss seems to be fitting the bill.
This does not sound like a location where you will ever be able to grow healthy grass. If you think the moss is ugly, you could try using pebbles as a mulch or perhaps try establishing a ground cover. Another option is to accentuate and take advantage of the moss "carpet" effect by adding an attractive bench and a large container of shade tolerant annuals for summer color. I hope this gives you some ideas.
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