How to simplify trigonometric inequality? $| 3 ^ { \tan ( \pi x ) } - 3 ^ { 1 - \tan ( \pi x ) } | \geq 2$

This is equivalent to $(y^2-3)^2\ge4y^2$ with $y=3^{\tan(\pi x)}$. The situation of $y^2$ with respect to the roots of the polynomial $(z-3)^2-4z=(z-9)(z-1)$ yields the sign of the polynomial. As a result, the inequality holds if $\tan(\pi x)\le0$ or $\tan(\pi x)\ge1$. That is, the fractional part of $x$ should not be $\frac12$ nor in $(0,\frac14)$.
