Kirk,
I have entered a bug report for your Solve problem
(https://sourceforge.net/tracker/index.php?func=detail&aid=850884&group_
id=4933&atid=104933), and have found a workaround for you.
Here's a transcript:
(C1) d: %pi/6$ 6
(C2) g1: %pi/3$ 3
(C3) g2: %pi/4$
(C5) [(u+cos(d)*sec(g1))^2+(v-sin(d)*sec(g1))^2=(tan(g1))^2,
(u+sin(d)*sec(g2))^2+(v-cos(d)*sec(g2))^2=(tan(g2))^2];
2 2
(D5) [(v - 1) + (u + SQRT(3)) = 3,
SQRT(3) 2 1 2
(v - -------) + (u + -------) = 1]
SQRT(2) SQRT(2)
(C6) ratsimp(d5);
2 2
(D6) [v - 2 v + u + 2 SQRT(3) u + 4 = 3,
2 2
v - SQRT(2) SQRT(3) v + u + SQRT(2) u + 2 = 1]
(C7) [d6[1],d6[1]-d6[2]];
2 2
(D7) [v - 2 v + u + 2 SQRT(3) u + 4 = 3,
SQRT(2) SQRT(3) v - 2 v + 2 SQRT(3) u - SQRT(2) u + 2 = 2]
(C8) solve(%,[u,v]);
(D8) [[u =
(SQRT(2) SQRT(3) + 3) SQRT(9 SQRT(2) SQRT(3) - 22) - SQRT(3)
------------------------------------------------------------,
6
v = - ((7 SQRT(3) + 9 SQRT(2)) SQRT(9 SQRT(2) SQRT(3) - 22)
- 2 SQRT(2) SQRT(3) - 3)/6], [u =
(SQRT(2) SQRT(3) + 3) SQRT(9 SQRT(2) SQRT(3) - 22) + SQRT(3)
- ------------------------------------------------------------,
6
v = ((7 SQRT(3) + 9 SQRT(2)) SQRT(9 SQRT(2) SQRT(3) - 22)
+ 2 SQRT(2) SQRT(3) + 3)/6]]
You can change the form of this using various other Maxima functions,
including radcan, factor, rootscontract, expand, etc.
By the way, using the same techniques, you can solve the equations for
*general* values of d, g1, g2. Judicious use of trigsimp, trigreduce,
etc. (both before and after solving) makes the solution reasonably
sized.
-s