Find all points of intersection of the curves $r=2$ and $r=2\cos(2\theta).$

Use the following format to input your answers:

(1) Give your answer in polar coordinates $(r,\theta)$ with $r>0$ and $0 \le \theta < 2\pi.$

(2) If the pole is an intersection point, type "pole" in lower case letters in both blanks for the first intersection point.

(3) List all other intersection points in order of increasing $r.$ If more than one point has the same value of $r,$ list these points in order of increasing $\theta.$

(4) Type a capital "N" in all unused blanks.

First intersection point: $(r,\theta) =$ (, )

Second intersection point: $(r,\theta) =$ (, )

Third intersection point: $(r,\theta) =$ (, )

Fourth intersection point: $(r,\theta) =$ (, )

Fifth intersection point: $(r,\theta) =$ (, )