Classify the singularities of the following functions at both $z=0$ and at the point at infinity on the extended complex plane:

$$\begin{aligned} f_{1}(z) &=\frac{e^{z}}{z \sin ^{2} z}, \\ f_{2}(z) &=\frac{1}{z^{2}(1-\cos z)}, \\ f_{3}(z) &=z^{2} \sin (1 / z) \end{aligned}$$