how to fill page with hexagons?

[shokan22]

I just tried to fill a page with black-filled hexagons so that they are all aligned perfectly vertically and horizontally. I duplicated and positioned as best I could by hand. Then, I used Alignment>equispace on horiz row selections then vert selections. No matter what I do, it will never be perfect with hand placement, obviously.

Is there a way to fill a page with the hexagons so that it looks like the attachment (ie everything perfectly squared in respect to the page)? I would need perfectly uniform spaces between the shapes so that it comes out perfectly squared with the page. This would be the first step I need to do in making a seamlessly tiled alpha for ZBrush.