The mistake you made was that you multiplied (1-3t^2x) on both sides of the inequality without considering the sign of the term mentioned.If it is negative,the inequality sign will reverse.It is better to avoid such multiplication when there is a possibility that the term you are multiplying can change sign.So you should consider 2 cases one for +ve and other for -ve sign.In this problem the better method would be to take the term (3-t^2x)/(1-3t^2x)=y and simplify it to a quadratic eqn.Now since tanx is real,put that condition in discriminant D>0 and get the answer.
Moderation Team
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