What is the answer of $\inf\limits_{k\geq 1,k\in \mathbb{N}} |\sin(k^2)|$? It may be $0$, just like $\inf |\sin(k)| = 0$ for $k\geq 1,k\in \mathbb{N}$. How to prove it?
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Related question https://math.stackexchange.com/questions/2325386/can-we-extend-the-proof-of-density-of-sinn-to-sinn2 – Robert Z Jul 29 '19 at 13:40