Zeros of entire function

Question

I have an entire function $f $, whose restriction to $\mathbb C \setminus \{0\}$ is defined by $$f (z)=\frac {\sin z-z} {z^3}.$$ I must show that it has infinite zeros. Clearly it has order $1$; I think that I should use Hadamard factorization theorem, but I can't see clearly how to proceed. I'd like just a hint to start with, thank you in advance