Wild birds eating eggs

[rios_jss]

My hens are free range and need access to their nesting boxes. Recently, several types of wild birds have discovered that they can get a quick meal by breaking into uncollected eggs. I collect 2-3 times/day but they’re still getting several a day. I’ve reduced the size of the access to just big enough for a chicken but they still get in. Anyone have luck with discouraging wild birds? Do roosters help? I don’t have one.

 

[BDutch]

What kind of wild birds? I think that might be important.
Are you sure there aren’t brown birds with a long pink and naked tail amongst them? Or birds that aren’t any wilder than your chickens who lay an egg almost every day?
I know rats, snakes and chickens are common egg stealers.