Let $ theta = min {t mid X_ {t} + t not in (0,1) } $ represent the first time when $ Y_ {t} = X_ {t} + t $ does not belong to $ (0, 1) $. Calculate $ P_ {x} {Y _ { theta} = 0 } $, or $ X_ {0} = x in (0, 1) $

I'm trying to calculate the probability that we would reach the $ 0 limit before the $ 1 $ limit, I believe. I could not find too many similar examples and would appreciate help. I do not really know how to start.

Some examples I saw only deal with a Brownian motion striking the limit, but there is a $ t $ term here. I would appreciate a lot of help because I study for an exam. I think this problem is related to Ito's lemma.