Numerical Methods: Euler to Runge–Kutta · Challenge problem

The $\theta$-method $y_{n+1} = y_n + h\left[(1 - \theta)f(t_n, y_n) + \theta f(t_{n+1}, y_{n+1})\right]$ with $\theta = \dfrac{1}{3}$ is applied to $y' = -2y$. What is the largest step size $h$ for which the iterates do not grow in size?