We estimate parameter $\theta$ based on the measurements of two points $(X_1, Y_1)$ and $(X_2, Y_2)$ for the following linear model: $$\begin{cases} \hat{X_1} \theta = \hat{Y_1} \, ,\\ \hat{X_2} \theta = \hat{Y_2} \ , \\ X_1 = \hat{X_1}+\epsilon_1 \ , \\ X_2 = \hat{X_2}+\epsilon_2 \ , \\ Y_1 = \hat{Y_1} + f_1 \ , \\ Y_2 = \hat{Y_2} + f_2 \ . \end{cases} $$ Where $\epsilon_1, \epsilon_2, f_1, f_2 \sim \mathcal{N}(0,\sigma^2)$ are IID measurement errors and $\hat{X_1}, \hat{X_2}, \hat{Y_1}, \hat{Y_1}$ are means (true values) of the measurements.
The ordinary least squares method has the following estimation: $$\theta_{OLS} = \frac{Y_1 X_1 + Y_2 X_2}{X_1^2 + X_2^2} \ .$$
What is the mean for $\theta_{OLS}$?