Now note that the following becomes good approximations as θ→0:

sinθ≈θ
sin2(π4−θ)≈12−c⋅θ
(where c is some constant.) Use these approximations to estimate the probability of success of the two measurements as x→0 (as a function of x and c).

Measurement I:
Measurement II:

Why are you taking that course if you can't understand anything from it? It's so bad that you were unable to copy the required information for the problem to be solved...