Find all singularities of$ \ \frac{\cos z - \cos (2z)}{z^4} \ $ How do I find all singularities of$
\
\frac{\cos z - \cos (2z)}{z^4}
\
$
It seems like there is only one (z = 0)?
How do I decide if it is isolated or nonisolated?
And if it is isolated, how do I decide if it is removable or not removable?
If it is non isolated, how do I decide the orders of the singularities?
Thanks!!!

$$\cos z = 1-\frac{z^2}{2}+\cdots$$
$$\cos2z=1-\frac{(2z)^2}{2}+\cdots$$
$$\frac{\cos z-\cos2z}{z^4}= \frac{3}{2z^2}+\left(\frac{-15}{4!}+a_1z^2 +\cdots\right),$$
hence at $z=0$ there is a pole .
