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I think, either continuously get developer beta updates and update to iOS 11 when it is released in September.
Can’t switch to public beta from developer beta
 
Kind of. You can just remove the dev profile and install the public beta profile. In the case of my iPad, there wasn't new update (same build?) but my iPhone 5s I have kicking around on iOS 11 beta 2 got an update when I switched to the public beta.
 
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