T=T1+T2 is still a uniform distribution (I'll let you think over which interval).
Then T3=T+G, where G follows a geometric distribution (because it will give the time you get a taxi)
So T3-T ~ G(1/2)
First condition with respect to T and find the pdf of T3|T.
Then use this formula : and .
Looks a bit complicated, but not that much.