The formulae certainly provide all the items I found by brute force. Here's a look at what is produced, showing m,n, a,b,c and the ratio of angles (all are 3). Only those where the triangle inequalities hold and gcd(a,b,c)=1 are shown. Values of m and n were used only up to 50, so some cases of m may stop at n=50 only due to this.
2 3 10 8 3 3
3 5 48 27 35 3
4 7 132 64 119 3
5 8 195 125 112 3
5 9 280 125 279 3
6 11 510 216 539 3
7 10 357 343 20 3
7 11 504 343 253 3
7 12 665 343 552 3
7 13 840 343 923 3
8 13 840 512 533 3
8 15 1288 512 1455 3
9 13 792 729 91 3
9 14 1035 729 476 3
9 16 1575 729 1504 3
9 17 1872 729 2159 3
10 17 1890 1000 1513 3
10 19 2610 1000 3059 3
11 16 1485 1331 224 3
11 17 1848 1331 799 3
11 18 2233 1331 1476 3
11 19 2640 1331 2261 3
11 20 3069 1331 3160 3
11 21 3520 1331 4179 3
12 17 1740 1728 17 3
12 19 2604 1728 1387 3
12 23 4620 1728 5543 3
13 19 2496 2197 437 3
13 20 3003 2197 1240 3
13 21 3536 2197 2163 3
13 22 4095 2197 3212 3
13 23 4680 2197 4393 3
13 24 5291 2197 5712 3
13 25 5928 2197 7175 3
14 23 4662 2744 3151 3
14 25 6006 2744 5825 3
14 27 7462 2744 9099 3
15 22 3885 3375 748 3
15 23 4560 3375 1817 3
15 26 6765 3375 5876 3
15 28 8385 3375 9352 3
15 29 9240 3375 11339 3
16 23 4368 4096 391 3
16 25 5904 4096 2825 3
16 27 7568 4096 5859 3
16 29 9360 4096 9541 3
16 31 11280 4096 13919 3
17 25 5712 4913 1175 3
17 26 6579 4913 2548 3
17 27 7480 4913 4077 3
17 28 8415 4913 5768 3
17 29 9384 4913 7627 3
17 30 10387 4913 9660 3
17 31 11424 4913 11873 3
17 32 12495 4913 14272 3
17 33 13600 4913 16863 3
18 29 9306 5832 5597 3
18 31 11466 5832 9703 3
18 35 16218 5832 20195 3
19 27 6992 6859 189 3
19 28 8037 6859 1736 3
19 29 9120 6859 3451 3
19 30 10241 6859 5340 3
19 31 11400 6859 7409 3
19 32 12597 6859 9664 3
19 33 13832 6859 12111 3
19 34 15105 6859 14756 3
19 35 16416 6859 17605 3
19 36 17765 6859 20664 3
19 37 19152 6859 23939 3
20 29 8820 8000 1189 3
20 31 11220 8000 4991 3
20 33 13780 8000 9537 3
20 37 19380 8000 21053 3
20 39 22420 8000 28119 3
21 31 10920 9261 2449 3
21 32 12243 9261 4544 3
21 34 15015 9261 9316 3
21 37 19488 9261 18019 3
21 38 21063 9261 21356 3
21 40 24339 9261 28720 3
21 41 26040 9261 32759 3
22 35 16302 10648 8995 3
22 37 19470 10648 14837 3
22 39 22814 10648 21567 3
22 41 26334 10648 29233 3
22 43 30030 10648 37883 3
23 33 12880 12167 1023 3
23 34 14421 12167 3332 3
23 35 16008 12167 5845 3
23 36 17641 12167 8568 3
23 37 19320 12167 11507 3
23 38 21045 12167 14668 3
23 39 22816 12167 18057 3
23 40 24633 12167 21680 3
23 41 26496 12167 25543 3
23 42 28405 12167 29652 3
23 43 30360 12167 34013 3
23 44 32361 12167 38632 3
23 45 34408 12167 43515 3
24 35 15576 13824 2555 3
24 37 19032 13824 8029 3
24 41 26520 13824 21689 3
24 43 30552 13824 29971 3
24 47 39192 13824 49679 3
25 36 16775 15625 1656 3
25 37 18600 15625 4403 3
25 38 20475 15625 7372 3
25 39 22400 15625 10569 3
25 41 26400 15625 17671 3
25 42 28475 15625 21588 3
25 43 30600 15625 25757 3
25 44 32775 15625 30184 3
25 46 37275 15625 39836 3
25 47 39600 15625 45073 3
25 48 41975 15625 50592 3
25 49 44400 15625 56399 3
26 37 18018 17576 629 3
26 41 26130 17576 13489 3
26 43 30498 17576 21371 3
26 45 35074 17576 30285 3
26 47 39858 17576 40279 3
26 49 44850 17576 51401 3
27 40 23517 19683 5680 3
27 41 25704 19683 9143 3
27 43 30240 19683 16813 3
27 44 32589 19683 21032 3
27 46 37449 19683 30268 3
27 47 39960 19683 35297 3
27 49 45144 19683 46207 3
27 50 47817 19683 52100 3
28 41 25116 21952 4633 3
28 43 29820 21952 12083 3
28 45 34748 21952 20565 3
28 47 39900 21952 30127 3
29 42 26767 24389 3444 3
29 43 29232 24389 7181 3
29 44 31755 24389 11176 3
29 45 34336 24389 15435 3
29 46 36975 24389 19964 3
29 47 39672 24389 24769 3
29 48 42427 24389 29856 3
29 49 45240 24389 35231 3
29 50 48111 24389 40900 3
30 43 28470 27000 2107 3
30 47 39270 27000 19223 3
30 49 45030 27000 29449 3
31 44 30225 29791 616 3
31 45 32984 29791 4635 3
31 46 35805 29791 8924 3
31 47 38688 29791 13489 3
31 48 41633 29791 18336 3
31 49 44640 29791 23471 3
31 50 47709 29791 28900 3
32 47 37920 32768 7567 3
32 49 44064 32768 17297 3
33 47 36960 35937 1457 3
33 49 43296 35937 10927 3
33 50 46563 35937 16100 3
34 49 42330 39304 4361 3
re(6): NO DICE.....not a spoiler
