Последовательность синусов натуральных чисел

“I want to prove that $$\sup_{n \in \Bbb N}{\sin (n)} = 1$$

I was thinking of proving that some set related to $\pi$ is dense in $\Bbb R$ that will then imply there is some $n \in \Bbb N$ s.t….” (See below)

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