помогите решить 3tg^2 (x/3) - 2tg (x/3) -1 =0

Замените tg(x/3) на t:

3t - 2t - 1 = 0

t = 1

t = -1/3

--> tg(x/3) = 1, tg(x/3) = -1/3

--> x = 3π/4 + 3πk, x = -3arctg(1/3) + 3πk

Ответ: 3π/4 + 3πk; -3arctg(1/3) + 3πk