Find the third degree polynomial for f(x) = sec x around x=pi/4

i did this and got this
0 --> sec x
1 -->(sec x)(tan x)
2 -->(sec x)^3 + (sec x)(tan x)^2
3 -->(sec x) (tan x) ( 5 sec^2 x + tan^2 x)
when i plugged in pi/4 in them i didnt really see a pattern. i cant figure it out. HELP!!

You can use long division based on the expansion of cos(x).
cos(x) = 1 - x^2/2! + x^4/4! - ...
sec(x) = 1/[1 - x^2/2! + x^4/4! - ...] = 1 + x^2/2 + 5x^4/24 + ...