Demonstration- formula for angle between horizon and ecliptic

The most precise and quite intuitive formula I could find online is here: https://www.celestialprogramming.com/snippets/angleBetweenEclipticAndHorizon.html

$$\cos I = \cos ϵ \sin ϕ − \sin ϵ \cos ϕ \sin θ$$

ϵ is the obliquity of the ecliptic (e.g. 23.4°), ϕ is latitude, θ is the Local Sidereal Time.

Even though it makes sense that it depends on the sidereal time, latitude and inclination angle, I can't find a demonstration for this formula, so I'm wondering how can I demonstrate this formula?

• @astridlovespie Welcome to Stack Exchange! By "demonstrate" do you mean to plot it, or explain it, or derive it, or... We don't normally say "demonstrate a formula". Thanks!
– uhoh
Commented Jun 24, 2023 at 1:54
• Commented Jun 24, 2023 at 4:54
• Local sidereal time is an angle. 0 radians is when the plane of your local meridian passes the vernal equinox pi radians is 12 hours later. Commented Jun 24, 2023 at 22:24
• @ Greg Miller he may just be looking for the derivation. No one seems to know what he means by demonstration. His question is about your formula on a different site, Commented Jul 1, 2023 at 23:52