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Firstly you'll need to navigate to your channel settings- https://www.youtube.com/account_advanced
Then you'll need to copy your Channel ID.
You'll need to take that and paste it into the following embed code. Replace the YOURCHANNELID text with the Channel ID from your account page.
<iframe width="560" height="315" src="https://www.youtube.com/embed/live_stream?channel=YOURCHANNELID" frameborder="0" allowfullscreen></iframe>
Then you'll be able to paste that code into your website where you want it to display.
In Google Sites use code section of the Embed function.
See https://www.vmix.com/knowledgebase/article.aspx/213/how-to-embed-your-live-stream-onto-your-website
Embed a LivestreamClick the share button and copy the resultant code.
Full screen is unavailable when viewing outside of YouTube.