Solve the equation
$$\cot x-\tan x=4\cot(2x)$$
for $0^\circ<x<360^\circ$
My attempt,
$$\frac{1}{\tan x}-\tan x=4(\frac{1}{\tan 2x})$$
$$\frac{4(1-\tan^2x)}{2\tan x}-\frac{1}{\tan x}+\tan x=0$$
$$2-2\tan^2 x-1+\tan^2x=0$$
$$1-\tan^2x=0$$
$$\tan x=\pm1$$
$$x=45^\circ,135^\circ,225^\circ,315^\circ$$
So I've checked out with Desmos which I got
It shows that the answer is $45$ and$135$.
My questions:
1)Why my $225^\circ$ and $315^\circ$ are not included in the graph? Are they incorrect?
2)If I substitute the answers back to the equation, for example,
$$4\cot (2 \cdot 45)$$ which is undefined. Why?