Thread: angle between planes

Consider the following diagram:


The planes of all 4 orbits are inclined 30 degrees to the xy plane (I tilted the diagram a bit for clarity, so we're not looking from directly in the xy plane.

The green orbit and the purple orbit, although both inclined 30 degrees from the xy plane, are inclined 0 degrees from each other.

The orange orbit is rotated 180 degrees from the green and purple orbits. It appears to be inclined 60 degrees to the green and purple orbits.

The blue orbit is rotated 90 degrees with respect to the green and purple orbits. I'm guessing that it is inclined 30 degrees from the green and purple orbits and also 30 degrees from the orange orbit.

So in trying to come up with a formula to describe how one orbital plane is inclined relative to another my first guess is :

i1+cos(rotation)*i2
where i1 and i2 are inclinations of two planes relative to the xy plane.

Is this correct? Or would the relationship between rotation and inclination be linear instead of cosinusoidal? (is that a word, or is sinusoidal used for a cosine wave too?)

I think I've figured it out.
Asking around, I came up with this:
acos(sin(a1)sin(a2)cos(rot)+cos(a1)cos(a2))

Thanks to everyone who at least pondered this for me