I had this problem myself and I have overcome it without consulting a logopedist. At first I had trouble pronouncing even the word "tree", because the approximant /ɹ/ wouldn't work with the stop /t/. "Three" was even more difficult, because I wasn't used to the sound /θ/. I'd say that orange in mouth is a great metaphor here. This was exactly my feeling.
As I said, I don't have this problem now -- it's possible to overcome. Unfortunately, I'm not a specialist myself and it's difficult for me to give you any specific advice. Have you tried placing a schwa between [θ] and [ɹ], and then making it shorter and shorter? I think this could be the synthesis of how I solved my problem. I'm not sure though.
Do you have any trouble pronouncing the word "rarer"?
Please capitalize the word "I".
Student or Learner