How to send what's on my iPhone onto the big tv?

Ok so here's the set-up and what I have in mind.

Currently I'm living in France… I'm using a VPN changer for both my iPhone and my PS3 to watch Netflix US.

So the iPhone and PS3 are working well, and seem to be corresponding with each other flawlessly.

Now onto the problem:

I have some bluetooth speakers that (despite me researching and trying a couple of things) do not seem to be an option to connect to the PS3 - as an audio output (it will let me connect it as a bluetooth accessory - but, from what I understand, the PS3 will only accept bluetooth microphones in terms of audio.

So I'm trying to think of ways that I can get the speakers to play what is on the TV.

My iPhone connects perfectly to the speakers via bluetooth. So what I was thinking was that maybe there's a way that I can play the bluetooth audio from the iPhone so that it plays the audio from Netflix whilst watching the actual Netflix on my PS3.

It's important to note that I can, in fact, watch Netflix just on my phone with the bluetooth speakers.

The reason I thought that this might be a possiblity is because when I connect to Netflix on my phone, whilst it's open on the PS3, it allows me to wirelessly synchronise the two devices and therefore use the phone as a remote.

So, sorry to keep repeating myself but I'm in a rambling mood, can I also synchornise the audio - or does it simply not work like that.

Any help/tips/advice would be greatly appreciated.

Yes Chromecast.