I'm looking for an open source screen sharing that is web-based, are there any good options that I can look into?
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You can use BigBlueBUtton software. It is a free and opensource web conferencing software. there is no limit to share the number of webcams in a session.
OpenMeetings is the another opensource, web-based software. It provides screen sharing facility as well. It has been downloaded over 250,000 times.
Mconf is an open-source and free web conferencing system. It is an advanced and more customized version of BIgBlueButton. You can use this software too.