${\left( -\tan\left({\frac{ \sqrt{ 3 } }{ 3 }}\right) \right)}^{-1}$
A negative base raised to an odd power equals a negative$-{\tan\left({\frac{ \sqrt{ 3 } }{ 3 }}\right)}^{-1}$
Any expression raised to the power of $-1$ equals its reciprocal$-\frac{ 1 }{ \tan\left({\frac{ \sqrt{ 3 } }{ 3 }}\right) }$
Use $\frac{ 1 }{ \tan\left({t}\right) }=\cot\left({t}\right)$ to transform the expression$\begin{align*}&-\cot\left({\frac{ \sqrt{ 3 } }{ 3 }}\right) \\&\approx-1.53518\end{align*}$