To solve the given problem, we should start by analyzing the trigonometric equation and finding the required angle.

1. Given: \cos 2\theta = 0.
2. To find the value of \theta satisfying this equation with \theta as an acute angle, we use the property:
   • \cos 2\theta = 0 implies 2\theta = 90^\circ.
   • Therefore, \theta = \frac{90^\circ}{2} = 45^\circ.
3. Now, we need to find \sin(75^\circ - \theta):
4. Substitute the value of \theta:
   • \theta = 45^\circ; hence, we need \sin(75^\circ - 45^\circ) = \sin(30^\circ).
5. Using the known trigonometric value: \sin(30^\circ) = \frac{1}{2}.
6. Therefore, the value of \sin(75^\circ - \theta) is \frac{1}{2}.

Hence, the correct answer is \frac{1}{2}.