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

We know that the trigonometric ratio for cotangent is defined as:
$$\cot \theta =\frac{\text{Base}}{\text{Perpendicular}}=\frac{28}{45}$$

Let the Base ($B$) be $28k$ and the Perpendicular ($P$) be $45k$.
Using Pythagoras theorem, find the Hypotenuse ($H$):

$$H=\sqrt{P^2+B^2}$$

$$H=\sqrt{(45k{)}^2+(28k{)}^2}$$

$$H=\sqrt{2025k^2+784k^2}=\sqrt{2809k^2}=53k$$

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

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

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

Now substitute these values into the required expression:

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