Secant of 17pi/4 - Trig

I got the squareroot of two. The book says I'm absolutely wrong, and that it's the squareroot of 2 over two. I thought since four divides into 17 - 4pi times, with pi/4 left, and pi/4 left, meaning 45 degrees, and the secant of that being 1/squareroot of 2 over two, once rationalization of the denominator was finished, squareroot of two was left.

Where have I went wrong?

sec(t) =
1 / cos(t)

sec(17pi/4) =
1 / cos(17pi/4) =
1 / cos(4pi + pi/4) =
1 / cos(pi/4) =
1 / (sqrt(2) / 2) =
2 / sqrt(2) =
sqrt(2)

Your book is wrong. You are right.