Verified answer

3sin2x > 1

sin2x > 1/3

arcsin(1/3) + 2πk  <  2x <  π - arcsin(1/3) + 2πk, k∈Z

(1/2)*arcsin(1/3) + πk  <  x <  π/2 - (1/2)*arcsin(1/3) + πk, k∈Z