Why is $\pi/2$ omitted from the solution of $\cot x = 3 \sin 2x$?

Question

Why is it that the solution of $$\cot x = 3 \sin 2x \quad(\text{for the interval}\; -\pi < x < \pi)$$ does not include $\pi/2$, even though if this is graphed, it shows intersections at $x = \pm\pi/2$?

Please see graph below. (The solutions mentioned are only four, to the exclusion of positive and negative $\pi/2$.)

Algebraically as well, one of the factors comes out to be $\cos x = 0$ (which should give $x = \pi/2$). (Hence the graph.)

Answer 1

You are right the values $x=\pm \frac{\pi}2$ are solutions of the equation

$$\cot x=3 \sin 3x \implies \cot \pm\frac{\pi}2=3 \sin \pm\pi=0$$

maybe it was not included since it is considered a trivial solution.

added after editing

The values $x=\pm \frac{\pi}2$ seem to be indeed included among the solutions.

Answer 2

There is no reason for not including $x=\pm \pi/2$ in the intersection set.

Surprisingly enough they have the $x=\pm \pi/2$ as solultions but they did not list them as solutions because of the quadrant confusion.

Which quadrant are $x=\pm \pi/2??$ in??