there are several sizes or lenghts of drip edges and many colors avail.
The smaller version will go up under the first course of shingles fine. You can do this without any problem, but the wider versions will require some re nailing of the first course.
Remember, there is a up side and a down side on drip edges, if you are unsure, ask someone where you buy the material.
To nail the drip edge down, I use roofing nails or a 4 d box nail. Lift a tab up and make your nail there, then replace the tap and even squirt a bit of caulk tar on the head for good measure.
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