It’s a lot easier to just purchase a Chromecast stick, plug it to HDMI port of an HDTV, and then, just cast the smartphone screen to the TV. And, it looks a lot sharper and clearer. I do it all the time, and it’s a great ‘movie projector’.
That requires an HDTV, which is a bit more expensive than a shoebox.
I went your route.
I walked past my TV and it automatically connected to my phone.
It is smarter than me, and now I’ve exposed my 4 yr old to a perennial favorite: RC plane crashes.