Are you familiar with Relations? You could set 2 driving dimensions (of different orientations) equal to each other
e.g. &d23=&d41
(in this case d23 could be your 45º angle and d41 your 60º angle that you want. This way they would both be 60º, or if you turn them around vise versa so you can control which dimension drives which). An alternative is to just display a reference dimension on the dwg, which if you ever wanted to modify you could just go to the original feature in the model.