Need to find the angle between two planes

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Lets say, the rings A & B are on top of each other, I say there are completely ordered. If they are side by side (Like both rings on a same plane), then I say they aren't ordered at all. If I just calculate the angle between the normals, then In both cases I get zero degrees. I use tcl scripting to code this. I want to distinguish these both cases based on the angle.

One way of doing it is to draw a line joining the centers and find the angle between the line and the plane. But I found that it isn't giving accurate angle for reason I cannot figure it out. Any other approach to find this?