6. (a) Find the Taylor series expansion about \(\frac { \pi } { 4 }\) of \(\tan x\) in ascending powers of \(\left( x - \frac { \pi } { 4 } \right)\) up to and including the term in \(\left( x - \frac { \pi } { 4 } \right) ^ { 3 }\).
(b) Deduce that an approximation for \(\tan \frac { 5 \pi } { 12 }\) is \(1 + \frac { \pi } { 3 } + \frac { \pi ^ { 2 } } { 18 } + \frac { \pi ^ { 3 } } { 81 }\)