It’s important that the “angle” isn’t directly the fraction of c, but tanh^-1(v/c). This number is also called “rapidity”, and goes to infinity as v -> c. Yes,

It’s important that the “angle” isn’t directly the fraction of c, but tanh^-1(v/c). This number is also called “rapidity”, and goes to infinity as v -> c. Yes, hyperbolic angles aren’t limited to [0, 2 pi). You can’t rotate all the way to lightspeed, that would be rotation by an infinite angle. For any finite angle (i.e. speed below c), you can always add the angle of the bullet to get a new (finite) angle.