Simplify exactly. Give your answer as a fraction of lowest terms with rational denominator.

(i)  sin⁡(45∘)=\displaystyle {\sin{{\left({45}^{\circ}\right)}}}=

(ii)  sin⁡2(45∘)=\displaystyle {{\sin}^{{2}}{\left({45}^{\circ}\right)}}=

(iii)  sin⁡3(45∘)=\displaystyle {{\sin}^{{3}}{\left({45}^{\circ}\right)}}=

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