Understanding F-statistics in population genetics
I am a bit wobbly on the subject, but I think the most important bit of information is that they are re-parametrising Wright's (1951) hierarchical analysis of variation, "F-statistics," "hierarchical partitioning of variation," or "population parameters," depending on whom you ask. The parameters correspond as follows (on the bottom of p.1358): Fit=F, Fis=f, Fst=θ. 

The relationship arises given some assumptions. Crucially here, if Fis (or f) is a measure of departure from Hardy-Weinberg Principle, and all populations identically depart from HWP, then Fit = 1 - Hi/Ht. It follows that, 1 - Fit = Hi/Ht. As well, we can rewrite this, so that, Hi/Ht = (Hi/Hs)(Hs/Ht).

Together, you can (maybe) see that, 1-Fit = (1−Fis)(1−Fst). Substituting, 1-F = (1-f)(1-θ).

(I realise that this is not a complete answer, but you can rearrange it with some algebra to get the Weir&amp;Cockerham equation, I think).

[Update Oct 25, 2016]: it eventually yields f = (F-θ)/(1-θ). I think the posted question (above) contains a typo--specifically a missing division operator. Perhaps someone missed the stroke on a typewriter in the original paper?