State exact trig values at special angles

1. 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 $$2 \cos x = \tan 2 x$$
2. 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 $$2 \cos x = \tan 2 x$$
1. 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.)
2. State with a reason whether this approximation is an underestimate or an overestimate.