Given that
sin theta = cos (theta - 45) ... ...(1)
As we know that for acute angle
sin theta = cos (90 - theta) .... (2)
On Comparing Eq (1) and (2)
cos (theta - 45) = cos (90 - theta)
Therefore
theta - 45 = 90 - theta
2(theta) = 90 + 45 = 135
theta = 135/2 = 67.5
Therefore theta is 67.5