14. Find the values of \(\theta\), to 1 decimal place, in the interval \(- 180 \leq \theta < 180\) for which $$2 \sin ^ { 2 } \theta ^ { \circ } - 2 \sin \theta ^ { \circ } = \cos ^ { 2 } \theta ^ { \circ }$$ [P1 January 2002 Question 3]
\includegraphics[max width=\textwidth, alt={}, center]{9f1194cd-cc8a-4f8d-8010-c62fea344c4e-10_835_974_379_438} Figure 1 shows a gardener's design for the shape of a flower bed with perimeter \(A B C D\).
\(A D\) is an arc of a circle with centre \(O\) and radius 5 m .
\(B C\) is an arc of a circle with centre \(O\) and radius 7 m .
\(O A B\) and \(O D C\) are straight lines and the size of \(\angle A O D\) is \(\theta\) radians.

1. Find, in terms of \(\theta\), an expression for the area of the flower bed. Given that the area of the flower bed is \(15 \mathrm {~m} ^ { 2 }\),
2. show that \(\theta = 1.25\),
3. calculate, in m , the perimeter of the flower bed.
   (3) The gardener now decides to replace arc \(A D\) with the straight line \(A D\).
4. Find, to the nearest cm , the reduction in the perimeter of the flower bed.
   (2)