I feel ridiculous asking this question because I know how simple it is, yet I can't seem to get the answer the book is getting.
Write this in a trigonometric form: -7 + 4i
it is just a matter of knowing that this is the reference angle of the one you want. you want the positive angle measured from the positive real-axis. so you need the angle which arctan(4/7) is a reference angle for, which is $\displaystyle \pi - \arctan \frac 47 \approx 2.62$