Cálculo de cosecante sin calculadora

$$\begin{gathered} \text{cosec} 120º=\text{cosec}\left(2·60º\right)=\frac{1}{2·\sin 60º·\cos 60º}\Rightarrow \\ \text{cosec} 120º=\frac{1}{2·{\displaystyle \frac{\sqrt{3}}{2}}·{\displaystyle \frac{1}{2}}}\Rightarrow \\ \underline{\text{cosec} 120º=\frac{2}{\sqrt{3}}} \end{gathered}$$