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\includegraphics[max width=\textwidth, alt={}, center]{17ca6dd2-271b-4b06-8433-354493feaf06-10_401_561_260_790} The diagram shows a rectangle \(A B C D\) in which \(A B = 5\) units and \(B C = 3\) units. Point \(P\) lies on \(D C\) and \(A P\) is an arc of a circle with centre \(B\). Point \(Q\) lies on \(D C\) and \(A Q\) is an arc of a circle with centre \(D\).

1. Show that angle \(A B P = 0.6435\) radians, correct to 4 decimal places.
2. Calculate the areas of the sectors \(B A P\) and \(D A Q\).
3. Calculate the area of the shaded region.