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I believe the math is right, but there is a wrinkle you should take into account.
The more the number of joints increases, the larger will be the effect of any errors in making the cuts, even though each error is itself small. Errors creep into these cuts two ways: the first involves any error in your miter scale, so make sure you have calibrated it well. The less obvious error is the tiny creep that the blade induces in the stock as it bites into it; you probably can't hold the stock tight enough if you try to do it by hand against the miter fence (and a death grip can be dangerous): so use a solid hold-down clamp.