Solve the equation: 3tg²x + tgx - 2 = 0

Let t = tgx. Then 3t² + t - 2 = 0. The roots are t = -1 and t = 2/3. Therefore, tgx = -1 and tgx = 2/3. Solutions: x = -π/4 + πn, x = arctg(2/3) + πn, n∈Z.