To show a triangle in LaTeX, the code is \bigtriangleup, not \triangle:
\(\displaystyle \bigtriangleup ABC\)
Let tan A = k, tan B = 2k, and tan C = 3k. Since we have a triangle ABC, use the identity
\(\displaystyle \tan A + \tan B + \tan C = \tan A \tan B \tan C\),
make substitutions, and solve for k. (There will actually be 3 solutions for k, but only one will be valid.) You'll then find that angle A is a special angle. Angles B and C are not "nice" angles (not whole numbers in degrees), however.