**1-1**
For any \(\epsilon >0\), Prove that there exists \(\sin { (n) } <\epsilon\) where n is natural number. (If \(\epsilon >1\), this is trivial.)

**1-2**
Prove that there are infinitely many natural number n that satisfies **1-1**

**2**
Using above, prove that \( \limsup _{ n\rightarrow \infty }{\sin { (n) } } =1\).

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