Yes, rarely but yes
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No, the egg will not be shiny. However, it is possible that the egg will hatch into a shiny Pokemon, but the chances of getting a shiny Pokemon from the egg are not any higher than they would be if the ditto were not shiny.
There is a chance, but not usually. You can get shinies from eggs of normal colored Pokemon, but that's even rarer than encountering a shiny or getting a shiny from an egg laid by a shiny
There is no way of telling if a Pokemon in an egg is shiny until it hatches. Sorry.
you just have to encounter the Pokemon that is going to hatch out of the egg about 1000 times and if your lucky it'll be a shiny Pokemon hope this helped:)
Getting a shiny egg is like getting a needle in a hay stack.