Couple of points. * It’s not trigonometry. The inverse of a proper ellipsoidal Mercator has no closed-form solution. * Data generally are in geographic coordinates, not map coordinates. If your data are in map coordinates, then definitely do not use Web Mercator unless your map coordinates are also Web Mercator. The same is true for any projection: You need to know what coordinates your source data are in (Geographic? Than what datum? Or map? Then what projection?). If there is a mismatch between your data coordinates and the projection you’re using, you have to convert between them. Web Mercator adds nothing new to that problem. * There is nothing “inconsistent” about Web Mercator formulas.