Setup tv-soundbar-beamer-chromecast 4k

I have a chromecast which i connect to both tv and beamer (using a switch).
At this moment chromecast is connected to tv. Tv and soundbar are connected using HDMI-ARC. Soundbar (Signa 4) only has 1 hdmi in/output.

Now i bought a beamer, which has no ARC support. How do I connect the beamer to the soundbar without losing audio quality. Still want to be able to hear Dolby Atmos :smile:

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