Identifying trichroic crystal systems
Theoretical answer:

You need to measure extinction angles. If it is always extinct when aligned to cleavage or crystal faces, then it is orthorhombic. If it sometimes aligns and the colour is consistent, it's monoclinic. Otherwise it's triclinic. You do not need to know how cleavage is oriented with respect to the axes in advance because there very few orthorhombic minerals with oblique cleavage (if any at all).

Practical answer (and a rant):

I have no idea why is this still taught in 2016. The motivation of this thing is to know optical properties so you can derive chemical information from them. These days it's probably cheaper and faster to put the sample in XRD or SEM-EDS to know what it is. Even when three colours exist, it is usually very subtle and you will need a lot of self-convincing to see the third colour on its own and not as a combination of the other two. Then there's the issue of a real mineral actually having a proper crystal shape and cleavage (good luck doing this on a 10 micrometre wide anhedral crystal in a thin section).