Ugly Or Beautiful Expression

$Sin(1) = \dfrac {1}{2} ie^{- \frac{i \pi}{180}} - \dfrac{1}{2} ie^{ \frac{i \pi}{180}}$

$\Rightarrow \dfrac{1}{2i} \left( - (e^{- \frac{i \pi}{2}})^{\frac{1}{90}} + (e^{ \frac{i \pi}{2}})^{\frac{1}{90}} \right)$

$\Rightarrow \dfrac{1}{2i} \left( - (-i)^{\frac{1}{90}} + (i)^{\frac{1}{90}} \right)$

$\Rightarrow \dfrac{1}{2i} \left( - ( 0.99984...- 0.01745... i ) + ( 0.99984... - 0.01745... i ) \right) \approx 0.01745...$

Problem is that when taking the $n$ th root of a complex number, there are $n$ possible answers, not just one.