How do I find the principle value of the argument of ?
No. The argument is an angle (in this case, 4 radians). But an angle is only determined up to a multiple of 2π. The principal value of the argument is obtained by taking the value of the argument that lies in some specified interval of length 2π, usually the interval $\displaystyle (-\pi,\pi]$. So if 4 lies in that interval then the principal value is just 4. Otherwise, you'll have to add or subtract a multiple of 2π to 4 in order to bring it into that interval.