In reply to some off-line queries, here is a cleaned up re-writing of my
previous post:
If Earth and Venus start out in conjunction at t=0 and Theta=0, then at
t=584
(prox) earth days they will again be in conjunction, but now at Theta =
216 degrees (prox), Earth/Venus having gone through 1.6/2.6 revolutions
around the sun.
In this time Venus will have rotated about 584/243=2.4 times on its own
axis.
This extra .4 of a retrograde rotation is .4*360=144 degrees. Since
144+216=360, this is just how much Venus must be turned to again look
at earth with the same face, when both are at Theta=216 degrees.
I hope that takes care of the typo boo-boos and makes my reasoning clear.