Write down the exact values of \(\cos \frac { 1 } { 6 } \pi\) and \(\tan \frac { 1 } { 3 } \pi\) (where the angles are in radians). Hence verify that \(x = \frac { 1 } { 6 } \pi\) is a solution of the equation
$$2 \cos x = \tan 2 x$$
Sketch, on a single diagram, the graphs of \(y = 2 \cos x\) and \(y = \tan 2 x\), for \(x\) (radians) such that \(0 \leqslant x \leqslant \pi\). Hence state, in terms of \(\pi\), the other values of \(x\) between 0 and \(\pi\) satisfying the equation
$$2 \cos x = \tan 2 x$$
Use the trapezium rule, with 3 strips, to find an approximate value for the area of the region bounded by the curve \(y = \tan x\), the \(x\)-axis, and the lines \(x = 0.1\) and \(x = 0.4\). (Values of \(x\) are in radians.)
State with a reason whether this approximation is an underestimate or an overestimate.