Monotonicity conjecture for the intersection angle

For $p\in(0,\sqrt{3}/2)$, let $\alpha(p)$ denote the angle at which the trajectory of the relevant solution intersects the $\varphi_0$-axis for the first positive intersection.

Monotonicity conjecture. The angle $\alpha(p)$ is a monotone function for

$$p\in(0,\sqrt{3}/2).$$

This conjecture is introduced as part of a numerical argument intended to rule out the interval $(0,\sqrt{3}/2)$ when determining which periodic solutions correspond to extremal metrics. The supplied text does not state whether the conjecture has been proved or disproved.