Use the trapezium rule with two intervals to estimate the value of
$$\int _ { 0 } ^ { \frac { 1 } { 3 } \pi } \sec x \mathrm {~d} x$$
giving your answer correct to 2 decimal places.
Using a sketch of the graph of \(y = \sec x\) for \(0 \leqslant x \leqslant \frac { 1 } { 3 } \pi\), explain whether the trapezium rule gives an under-estimate or an over-estimate of the true value of the integral in part (i).