Here's an equivalence from Veach's thesis on light transport (page 88, 3.16): $$|\cos(\theta)|\sin(\theta)d(\theta)d(\phi) \equiv \\ \sin(\theta)d(\sin(\theta))d(\phi)$$
This seems wrong in the general case since the absolute value is dropped. Also, $\theta$ is assumed to be in $[0,\pi]$ (as can be seen in 3.17), so this definitely doesn't seem like it can be done. I just want somebody to confirm that this is indeed a typo. The thesis can be found here: http://graphics.stanford.edu/papers/veach_thesis/
P.S. I have no idea how to change the name of the link, tried [url] and < a >.
That does look like a typo to me, at least for $\omega \cdot N < 0$; for the case where you're studying scattering by reflection, however, it might be useful.