You can make a YouTube Live stream autoplay in fullscreen on your playlist by following the steps below. Please note this does not work for every live stream as it may be restricted by the channel itself.
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After finding the desired Live Stream URL, type “_popup” just after “watch” on the URL then press the enter key.
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Now type “?autoplay=1” at the end of the URL followed by pressing the enter key.
The URL will now start autoplaying in fullscreen and can be set up with the Website Zone on your playlist.