The spinning disks

This is one of the puzzles I wrote back in the day.  It involves a decent amount of logic and a touch of cleverness.

I have this disk.  It's shaped like a CD, and divided into twelve sectors.  Some of those sectors are opaque, and some are transparent.  But the opaque and transparent sectors are not arranged in the particular order shown above.

Actually, I have two disks like this.  They're completely identical to each other.

I place the two disks on top of each other.  You can see through some sectors and not through others.  And then I begin to spin the top disk.  Every time it rotates one twelfth of a full circle, the number of transparent sectors changes.  It forms a sequence of numbers.

Here's part of the sequence:
..., 2, 3, 4, 4, 0, 4, ...

Which sectors of the disk are transparent, and which are not?

Solution posted