Variance proportional to a regressor squared: divide it out

You have strong reason to believe the error variance grows with the square of a positive regressor: $\operatorname{Var}(\varepsilon_i \mid x_i) = \sigma^2 x_i^2$.

Show how a simple transformation turns this into a constant-variance regression, and explain what estimator that yields and why it is preferable to OLS with robust standard errors.