$$\frac { \mathrm { d } ^ { 3 } y } { \mathrm {~d} x ^ { 3 } } = \sec x \tan x \left( p \sec ^ { 2 } x + q \right)$$
where \(p\) and \(q\) are integers to be determined.
Hence determine the Taylor series expansion about \(\frac { \pi } { 3 }\) of sec \(x\) in ascending powers of \(\left( x - \frac { \pi } { 3 } \right)\), up to and including the term in \(\left( x - \frac { \pi } { 3 } \right) ^ { 3 }\), giving each coefficient in simplest form.
Use the answer to part (b) to determine, to four significant figures, an approximate value of \(\sec \left( \frac { 7 \pi } { 24 } \right)\)