1.1. Given that $\theta$ is small, and that terms involving ${ \theta }^{3}$ or higher powers of $\theta$ can be ignored, show that

$\frac{1}{{cosec}^{2}(\frac{ \theta }{2})}+\frac{1}{{sec}^{2}(\frac{ \theta }{4})}\approx1+\frac{3}{16}{ \theta }^{2}$

1.2. Determine the percentage error when the result in part (a) is used to approximate

$\frac{1}{{cosec}^{2}(\frac{7}{20})}+\frac{1}{{sec}^{2}(\frac{7}{40})}$

giving your answer correct to 3 significant figures.