Split "map" into gps coordinate grid by certain kilometer number

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So I have a odd problem, which I can't really wrap my head around how to fix, mostly because I'm not that good at math I guess :-)

So lets say we have a map, any map, which has four corners, obviously. And this is a real-world map. And I would like to get every coordinate, by let's say a 15 kilometer interval on the entire map. How would I go about the math for that? Or is there a tool that can do this perhaps?

And we're talking long's and lat's here, not sure if that is important. And I don't really care about being precise, if it there is less than 2km error in the coordinates then I'm fine. I don't know if that makes it easier.

I did a shitty drawing to help explain, https://i.stack.imgur.com/yJZlO.jpg I am talking about all the "solid squares" those are the coordinates I would like, for an entire country as an example.

I'm hoping this problem will make sense, and someone can help me out here :-)

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