Prove or disprove: $\phi: \mathbb{N} \to \mathbb{N}\text{, }\phi(n) = \lfloor n \cdot | \sin( \sqrt{2} \cdot n ) | \rfloor$ is surjective

Question

How do I go about proving or disproving that the following function is surjective? Is there some sort of standard trick for integer functions?

$$\phi: \mathbb{N} \to \mathbb{N} \\ \phi(n) = \lfloor n \cdot | \sin( \sqrt{2} \cdot n ) | \rfloor$$

where $\lfloor x \rfloor$ denotes the function that returns the greatest integer less than or equal to $x$.

Thanks in advance.

(PS: it's not a homework question or anything, I'm just curious)