Suppose that we want to estimate the angles $\alpha, \beta$ and $\gamma$ (in radians, say) of the triangle $A B C$, based on a single independent measurement of the angle at each corner. Suppose that the error in measuring each angle is normally distributed with mean zero and variance $\sigma^{2}$. Thus, we model our measurements $y_{A}, y_{B}, y_{C}$ as the observed values of random variables

$$Y_{A}=\alpha+\varepsilon_{A}, \quad Y_{B}=\beta+\varepsilon_{B}, \quad Y_{C}=\gamma+\varepsilon_{C},$$

where $\varepsilon_{A}, \varepsilon_{B}, \varepsilon_{C}$ are independent, each with distribution $N\left(0, \sigma^{2}\right)$. Find the maximum likelihood estimate of $\alpha$ based on these measurements.

Can the assumption that $\varepsilon_{A}, \varepsilon_{B}, \varepsilon_{C} \sim N\left(0, \sigma^{2}\right)$ be criticized? Why or why not?