Answer
$\theta = tan^{-1}(\frac{4}{x})-tan^{-1}(\frac{1}{x})$
Work Step by Step
Let $\alpha_1$ be the small angle between the horizontal line and the bottom of the painting. Let $\alpha_2$ be the large angle between the horizontal line and the top of the painting.
$tan~\alpha_1 = \frac{1}{x}$
$\alpha_1 = tan^{-1}(\frac{1}{x})$
$tan~\alpha_2 = \frac{3+1}{x}$
$\alpha_2 = tan^{-1}(\frac{4}{x})$
We can write an expression for $\theta$:
$\theta = \alpha_2-\alpha_1$
$\theta = tan^{-1}(\frac{4}{x})-tan^{-1}(\frac{1}{x})$
