Calculate: tan(-(sqrt(3))/(3))^{-1}

Expression: ${\tan\left({-\frac{ \sqrt{ 3 } }{ 3 }}\right)}^{-1}$

Simplify the expression using the symmetry of trigonometric functions

${\left( -\tan\left({\frac{ \sqrt{ 3 } }{ 3 }}\right) \right)}^{-1}$

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

$\begin{align*}&-\cot\left({\frac{ \sqrt{ 3 } }{ 3 }}\right) \\&\approx-1.53518\end{align*}$