A uniform ladder leans against a smooth vertical wall, with its foot on a rough horizontal floor, as shown in the figure. The coefficient of static friction between the ladder and the floor is $0.4$. The ladder is placed at different angles $\theta$ with the floor. What is the smallest value of $\theta$ for which the ladder does not slip?

Fig. 1: A uniform ladder leaning against a smooth vertical wall, with its foot on a rough floor, making an angle theta with the floor.