is important to remark here that, despite its simplicity, we expect our model is more than adequate to investigate the qualitative trends that we would expect to observe in the data, and for providing order of magnitude estimates of the impact of triaxiality. Specifically, elliptical isothermal profiles appear to be excellent approximations to the true matter distribution in real lens systems [see e.g. @gerhardetal01; @rusinma01; @rusinetal03; @rusinkochanek05; @treuetal06; @koopmansetal06; @gavazzietal07], so the triaxial isothermal mass distribution considered here should provide a reasonably realistic model for order of magnitude estimates. While more sophisticated models are certainly possible [see e.g. @jiangkochanek07], it is our view that the simplicity of the isothermal model more than justifies our choice of profile for a first pass at the problem.

The Distribution of Halo Orientations for Triaxial Isothermal Profiles
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Before we look at the distribution of halo orientations, it is worth taking a minute to orient ourselves in the coordinate system we have chosen. Consider first Eq. \[eq:3dsie\]. The distance from the center of the halo to the intercept of a constant density contour is maximized for the $y$ axis, and minimized for the $z$ axis, while the $x$ axis is intermediate between the two. 