If $\cot \theta =\frac{28}{45}$, then find the value of $(\sin \theta -\cos \theta )$.

Given that:
$$\cot \theta =\frac{\text{Base}}{\text{Perpendicular}}=\frac{28}{45}$$

Let $\text{Base}=28$ and $\text{Perpendicular}=45$.

Using Pythagoras' theorem to find the hypotenuse:

$$\text{Hypotenuse}=\sqrt{{\text{Base}}^2+{\text{Perpendicular}}^2}$$

$$\text{Hypotenuse}=\sqrt{28^2+45^2}=\sqrt{784+2025}=\sqrt{2809}=53$$

Now, find the values of $\sin \theta$ and $\cos \theta$:

$$\sin \theta =\frac{\text{Perpendicular}}{\text{Hypotenuse}}=\frac{45}{53}$$

$$\cos \theta =\frac{\text{Base}}{\text{Hypotenuse}}=\frac{28}{53}$$

Calculate the required value:

$$\sin \theta -\cos \theta =\frac{45}{53}-\frac{28}{53}=\frac{45-28}{53}=\frac{17}{53}$$