Given theta = (1)/(3). We can construct a right-angled triangle where the opposite side is 1 and the adjacent side is 3.

Given $\tan \theta = \frac{1}{3}$. We can construct a right-angled triangle where the opposite side is 1 and the adjacent side is 3.
The hypotenuse $h$ is calculated using the Pythagorean theorem:

$$h = \sqrt{1^2 + 3^2} = \sqrt{1 + 9} = \sqrt{10}$$

Now we can find $\sin \theta$ and $\cos \theta$:

$$\sin \theta = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{1}{\sqrt{10}}$$ $$\cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{3}{\sqrt{10}}$$

The forces perpendicular to the inclined plane are the normal force ($N$) acting upwards and the component of gravity ($mg \cos \theta$) acting downwards into the plane. Since there is no acceleration perpendicular to the plane, these forces balance:

$$N - mg \cos \theta = 0$$ $$N = mg \cos \theta$$

The maximum static frictional force is given by $f_{s,max} = \mu N$, where $\mu$ is the coefficient of friction.

$$f_{s,max} = \mu (mg \cos \theta)$$

Substitute the given value of $\mu = \frac{1}{3}$:

$$f_{s,max} = \frac{1}{3} mg \left( \frac{3}{\sqrt{10}} \right) = \frac{mg}{\sqrt{10}}$$

The component of gravity pulling the brick down the incline is $mg \sin \theta$.

$$F_{down} = mg \sin \theta = mg \left( \frac{1}{\sqrt{10}} \right) = \frac{mg}{\sqrt{10}}$$

For the brick to move, the downward component of gravity must be greater than the maximum static frictional force ($F_{down} > f_{s,max}$).
In this case, we found:

$$F_{down} = \frac{mg}{\sqrt{10}}$$ $$f_{s,max} = \frac{mg}{\sqrt{10}}$$

Since $F_{down} = f_{s,max}$, the component of gravity pulling the brick down the incline is exactly equal to the maximum static frictional force. This means the net force along the incline is zero.
As the brick is released from rest, it will not start to move. Therefore, its acceleration is zero.
Applying Newton's second law along the incline:

$$\sum F_{\parallel} = ma$$ $$F_{down} - f_{s,max} = ma$$ $$\frac{mg}{\sqrt{10}} - \frac{mg}{\sqrt{10}} = ma$$ $$0 = ma$$

Since the mass $m$ is not zero, the acceleration $a$ must be zero.

$$a = 0 \, \text{m/s}^2$$

The acceleration of the brick is $\text{0 m/s}^2$.