3.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{f1efd9b3-d604-4088-a4b5-8680711aa8f1-08_353_474_301_781}
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\caption{Figure 1}
\end{figure}
Figure 1 shows a sketch of the curve \(C\) with equation
$$y = \frac { 1 } { 2 } ( \tan x + \cot x ) \quad \frac { \pi } { 6 } \leqslant x \leqslant \frac { \pi } { 3 }$$
- Show that the length of \(C\) is given by
$$\frac { 1 } { 2 } \int _ { \frac { \pi } { 6 } } ^ { \frac { \pi } { 3 } } \left( \tan ^ { 2 } x + \cot ^ { 2 } x \right) d x$$
- Hence determine the exact length of \(C\), giving your answer in simplest form.