#### Answer

Therefore, the value of $\theta$ is given by the function $f(x) = arctan(\frac{15}{x})-arctan(\frac{5}{x})$

#### Work Step by Step

Let $~A~$ be the angle between the wall and the right side of the board.
$tan~A = \frac{15}{x}$
$A = arctan(\frac{15}{x})$
Let $~B~$ be the angle between the wall and the left side of the board.
$tan~B = \frac{5}{x}$
$B = arctan(\frac{5}{x})$
We can find an expression for $\theta$:
$\theta = A-B$
$\theta = arctan(\frac{15}{x})-arctan(\frac{5}{x})$
Therefore, the value of $\theta$ is given by the function $f(x) = arctan(\frac{15}{x})-arctan(\frac{5}{x})$