We just had a new roof installed. I found this after. The new drip edge doesn't even go into the gutter, and the gutter is actually in front of the drip edge.
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What Is A Drip Edge?
Should a roof drip edge be placed above or below roofing felt? - Home Improvement Stack Exchange
drip edge installation details by Oldtimer4267, via Flickr | Roofing, Roof drip edge, Drip edge