The curves

are drawn below.

The curves intersect at $P$ and $Q,$ whose $x$ coordinates are $p$ and $q$ respectively.

1. Show that $p=\pi -\arctan (2)$ and $q=\pi .$

2. Using the trapezium rule with $5$ strips, approximate

   $${\int }_p^q\sin (2x)+1dx$$

   and

   $${\int }_p^q{\cos }^2(x)dx$$

3. Hence, find an estimate for the shaded area in the diagram.

Give your estimate for the shaded area to $2$ decimal places.