Numerical Methods: Euler to Runge–Kutta · Superchallenge 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 $\theta = \dfrac{1}{4}$ has absolute stability region $\{z \in \mathbb{C} : |R(z)| \le 1\}$, where $R(z)$ is its amplification factor on $y' = \lambda y$ with $z = \lambda h$. Find the area of this region.