@mdboom - I'm still not completely sure how this is supposed to work, but think you may need to deal with the `tunit is None` case as well. Likely, the only equivalency to use this will remain `dimensionless_angles`, and for this case, if, e.g., `other` has `radian` as a base, while `self` does not, should one not conclude this is a fair base to try?

I guess without further looking into this, I would suggest adding a test case:
```
u.Unit("rad/s").compose(units=(u.day,), equivalencies=u.dimensionless_angles())
```
but looking at the current master, this fails, so perhaps this is outside of the scope of this PR (if you think so, I'll make a separate issue).