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Wrong program. That's indeed what Illustrator or 2D CAD drafting programs are for. Setting up a hex grid as guides would be easy enough there, though in fact I'm sure your math (or your beloved one's) is somewhat crooked. In a system based on 60 degrees, all edges of the underlying triangles would have the same lengths and the combined lengths and distances would not be simple multiples with even factors. The explanatory images in this blog post should enlighten you:
For exact measurement in inches Illustrator is better as you only need option click on the canvas with a drawing tool to input your exact numeric values, or you can use the transform palette to edit them later.
Photoshop works in pixels only, and if you try to enter inches you get an error.
To get your angles I wold draw 2 lines and rotate them, then duplicate and reflect for 4 lines. You can then using snap to guides to get all the edges to touch accordingly, and use the live paint bucket to make your diamond
You could start with one inch square path, and make two duplicates. Transform them, changing either the width or height to 86.6% [one half the square root of three], and either the vertical or horizontal skew (depending on whether you changed to width or height) to thirty degrees:
One of the three you would also rotate 120 degrees. Each side will be one inch long.
Once you have the paths set up, you would then select each path in turn, and use them as vector masks for Color Fill layers, and with the Path Selection tool, step and repeat them to make your pattern as large as desired.