1. According to the plot, this happens twice for some [tex]x[/tex] between 135° and 180°, and for some [tex]x[/tex] between 270° and 315°.
We could try finding them exactly, but we would end up having to solve a 4th degree polynomial equation that doesn't factorize nicely...
2. Rewrite the inequality as
[tex]3\sin(x) - 2 > \tan(x) \implies 3 \sin(x) > \tan(x) + 2[/tex]
The curve [tex]y=3\sin(x)[/tex] lies above [tex]y=\tan(x)+2[/tex] when [tex]90^\circ < x < \alpha[/tex], where [tex]\alpha[/tex] is the first solution mentioned in (1) between 135° and 180°, approximately [tex]\alpha\approx151.127^\circ[/tex].
3. Rewriting
[tex]\tan(x) \ge 1 \implies \tan(x) + 2 \ge 3[/tex]
we see from the plot that this is true for [tex]x[/tex] between 45° and 90°, and again between 225° and 270°.
