Answer: Moss is an indication of compacted acidic soil, poor drainage, and excessive shade. You're wise in deciding to rototill and start over. While grass doesn't always thrive in shady areas, there are some grass varieties that are more shade tolerant than others and if you carefully prepare the soil prior to planting, it will perform well for you. Begin by rototilling the area and raking out the moss. Tilling in itself will go a long way in reducing the compaction and improving the drainage. You might also take the time to rototill in some organic matter to improve the tilth of the soil, as well. Once you've tilled and incorporated some organic matter, rake the area level and broadcast your grass seed (find a shade-tolerant grass mix at your local garden center). Once the grass is up and growing it should be mowed and watered regularly and fed 3-4 times a year. A lush, healthy lawn will crowd out most weeds.
Best wishes with your new lawn!
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