Don't worry about trying to trap the parent.

Just put down a foundation and four walls, and throw your eggs in the middle. If you have the mats, make a bigger box with higher walls, and throw the eggs in different places throughout. The parent will aggro on the eggs but struggle to reach them, which will buy you more time.

I trapped two parents of two different nests with one trap using this method and tamed both babies without aggroing the parents.

Bonus tip: if your eggs hatch, the parents will relentlessly attempt to kill whatever has hatched.

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