Question about gear oil for 6 spd TRD sport

Hey guys, first post- this forum is awesome.

I want to change the diff and tranny oil in my '07 TRD sport 4x4, 6 spd manual. I'm pretty sure it's a LSD in the back but I've heard the only good synthetic is royal purple. Is it better just to get Dino oil and add some LSD additive?

Also, any specs needed for the tranny change? Will that also take 75-90? And I'm thinking of using synthetic there but not sure if anyone has had any problems?

 

If it's an LSD they will be a tag I changed the trans fluid etc. with synthetic and there absolutely no difference shifted just as smooth as it did before.

 

Did you use LSD with the limited slip additive already in it?