To solve this equation for x, we can take the square root of both sides:

sin^2(x - π/4) = 0.75
sin(x - π/4) = ±√0.75
sin(x - π/4) = ±√3/2

Now, we need to find the values of x that satisfy this equation. Since sin(x - π/4) = ±√3/2, the possible solutions are:

x - π/4 = arcsin(√3/2) or x - π/4 = π - arcsin(√3/2)
x - π/4 = π/3 or x - π/4 = π - π/3
x = π/3 + π/4 or x = π + π/4 - π/3
x = 7π/12 or x = 5π/12

Therefore, the solutions to the equation sin^2(x - π/4) = 0.75 are x = 7π/12 or x = 5π/12.