I am about to open up registrations to my open-source meetup.com alternative, but am worried about the legal side.
What sort of things should I put in the Terms and Conditions, and do I need them to explicitly click "I agree" before being allowed to click "Register"?
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So we don't assume that your question is linkbait, What specifically about your terms and conditions are you concerned about? Is there something in Meetups T&C's that is problematic?
Here is an EFF article on the legality of different consent to agree approaches.
If you are worried about the legal side of your Terms and Conditions, shouldn't you hire an attorney to review yours??? Free legal advice here is not actual legal advice.
Second, take a look at your competitor's Terms and Conditions. How does yours differ?
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