The way you've described it you only have three joins. A-B, B-C and C-D (where A and D have one angled end while B and C have two). Each join is around 23 degrees and so you should end up around 69 degrees total.
Add an extra piece, or take it up to 15 degree cuts. I think that's getting a bit extreme though, so I'd rather more slices.
Hen
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