In very high pressure fittings, a 60 degree female cone (standard centre drill) is mated with a 59 degree male cone - this gives a line contact where the male and female meet, resulting in a high contact pressure.
I'm not suggesting you need to follow this principle, but if any uncertainty about the angle of the male cone, it's best to aim for a touch under 60 degrees, rather than allowing it to exceed 60 degrees.