Question: How to model Moon tilt illusion?

I never expected that the reflected light direction of sun from moon in the sky would be so dificult to imagine ...

at the following article mentioned :

we derive an equation for the magnitude of the moon tilt illusion that can be applied to all congurations of sun and moon in the sky.

THE MOON TILT ILLUSION

since the calculations contains many steps and high level mathematical formula , there is no way rather to recourse to maple (powerful math assistant )

I hope there was adaptations between a lots of functions and predefined schema of maple and this problem so that the calculations and visualization facilitated several times ?

your effort will be a graet present for all the people of the world that look to the moon crescent everytime !