If $\cot \theta =\frac{3}{4}$, $\theta$ is an acute angle, then $\sin \theta +\cos \theta -\tan \theta$ is equal to:

The correct answer is $\frac{1}{15}$.

Step 1: Understand the given trigonometric ratio.
We are given that $\cot \theta =\frac{3}{4}$, where $\theta$ is an acute angle.

In a right-angled triangle, cotangent is the ratio of the adjacent side to the opposite side:
$\cot \theta =\frac{\text{Adjacent}}{\text{Opposite}}=\frac{3}{4}$

Thus, we can assume:
Adjacent side = 3
Opposite side = 4

Step 2: Find the hypotenuse using the Pythagorean theorem.
${\text{Hypotenuse}}^2={\text{Adjacent}}^2+{\text{Opposite}}^2$

${\text{Hypotenuse}}^2=3^2+4^2=9+16=25$

$\text{Hypotenuse}=\sqrt{25}=5$

Step 3: Determine the required trigonometric ratios.
Since $\theta$ is an acute angle, all trigonometric values are positive:

$\sin \theta =\frac{\text{Opposite}}{\text{Hypotenuse}}=\frac{4}{5}$

$\cos \theta =\frac{\text{Adjacent}}{\text{Hypotenuse}}=\frac{3}{5}$

$\tan \theta =\frac{1}{\cot \theta }=\frac{4}{3}$

Step 4: Calculate the value of the given expression.
We need to evaluate $\sin \theta +\cos \theta -\tan \theta$:

$\sin \theta +\cos \theta -\tan \theta =\frac{4}{5}+\frac{3}{5}-\frac{4}{3}$

$=\frac{7}{5}-\frac{4}{3}$

Taking the common denominator (15):
$=\frac{7\times 3}{15}-\frac{4\times 5}{15}=\frac{21-20}{15}=\frac{1}{15}$

Hence, the required value is $\frac{1}{15}$.