4
\includegraphics[max width=\textwidth, alt={}, center]{96cc217a-ffb3-4764-946e-e32271784ad7-2_520_839_1795_653} In the diagram, \(A B C D\) is a parallelogram with \(A B = B D = D C = 10 \mathrm {~cm}\) and angle \(A B D = 0.8\) radians. \(A P D\) and \(B Q C\) are arcs of circles with centres \(B\) and \(D\) respectively.

1. Find the area of the parallelogram \(A B C D\).
2. Find the area of the complete figure \(A B Q C D P\).
3. Find the perimeter of the complete figure \(A B Q C D P\).
4. Given that $$3 \sin ^ { 2 } x - 8 \cos x - 7 = 0$$ show that, for real values of \(x\), $$\cos x = - \frac { 2 } { 3 }$$
5. Hence solve the equation $$3 \sin ^ { 2 } \left( \theta + 70 ^ { \circ } \right) - 8 \cos \left( \theta + 70 ^ { \circ } \right) - 7 = 0$$ for \(0 ^ { \circ } \leqslant \theta \leqslant 180 ^ { \circ }\).