Here is one way. The complementary angles way.

sinA = cos(pi/2 -A)

Likewise, tanA = cot(pi/2 -A)

So,

tan(3A) = cot(pi/3 -A)

Transform the LHS side into its cot form,

cot(pi/2 -3A) = cot(pi/3 -A)

So,

pi/2 -3A = pi/3 -A

pi/2 - pi/3 = -A +3A

pi/6 = 2A

A = pi/12 ------------answer.