Getting Euler (Tait-Bryan) Angles from Quaternion representation

After a lot of searching, I have finally found a reference that has what I needed. Although it doesn't appear in a 'Quaternion to Euler' or 'Quaternion to Tait-Bryan' google search, when I gave up and started looking for 'Quaternion to Axis-Angle' with the intention of going through that representation as an intermediate step, I came across the following wonderful document:

Technical Concepts
Orientation, Rotation, Velocity and Acceleration, and the SRM
Version 2.0, 20 June 2008
Author: Paul Berner, PhD
Contributors: Ralph Toms, PhD, Kevin Trott, Farid Mamaghani, David Shen, Craig Rollins, Edward Powell, PhD
http://www.sedris.org/wg8home/Documents/WG80485.pdf

It covers a lot of the formalisms, but most importantly, shows derivations and solutions for 3-1-3 and 3-2-1 Euler angle representation. It also seems to cover inter-conversion between pretty much every other rotation representation I'm aware of, and so I would also recommend it as a good general reference.

Oh, and the actual solution for a 3-2-1 ($z-y-x$) Tait-Bryan rotation convention from that reference: $$ \phi = \operatorname{arctan2}\left(q_2 q_3 + q_0 q_1,\frac{1}{2}-(q_1^2 + q_2^2)\right) \\ \theta = \arcsin(-2(q_1 q_3 - q_0 q_2)) \\ \psi = \operatorname{arctan2}\left(q_1 q_2 + q_0 q_3,\frac{1}{2}-(q_2^2 + q_3^2)\right) $$

Note that the gimbal-lock situation occurs when $2(q_1 q_3 + q_0 q_2) = \pm1$ (which gives a $\theta$ of $\pm \frac{\pi}{2} $), so it can be clearly identified before you attempt to evaluate $\phi$ and $\psi$.

(Convention for arctan2 is $\operatorname{arctan2}(y, x)$, as hinted on page 3.)