I'm following some online lecture notes on AREs and don't understand where a certain value came from. Consider a distribution function $F$ with a density function $f$ symmetric about $\theta$. We're considering two estimators, $\bar{X}_n$ (sample mean) and $\operatorname{Med} \lbrace X_1, X_2, \ldots, X_n\rbrace$
For large sample size $n$, I know that:
$$\bar{X}_n \sim N\left(\theta, \frac{\sigma_F^2}{n}\right) \text{ and } \operatorname{Med} \left\lbrace X_1, X_2, \ldots, X_n\right\rbrace \sim N\left(\theta, \frac{1}{4f(\theta)^2n}\right)$$
Hence it follows that $\operatorname{ARE}(\operatorname{Med}, \bar{X}) = 4f(\theta)^2\sigma_F^2$.
Now it says suppose $F \sim N(\theta, \sigma_F^2)$. Then $\operatorname{ARE}( \operatorname{Med}, \bar{X}) = \frac{2}{\pi} = 0.64$
Where is the $\frac{2}{\pi}$ coming from? I certainly believe it to be true, but I don't understand how that comes from the $4f(\theta)^2\sigma_F^2$.