The question

Find the first three non-zero terms of the Taylor series for sec(z) about 0.

My attempt

$\displaystyle f(z) = \frac{1}{cos(z)}$

Radius of convergence depends on the zeros of cos(z), so $\displaystyle |z| < \frac{\pi}{2}$

Now, I'm not sure how to proceed. I know the series for cos(z), but I'm not sure how to use it in this context. Any advice?