Yes, there is a quick and dirty 3-phase formula. While it is only truly accurate for perfect sine waves with 0, 120, and 240 degree phase spacing, it can be used in most applications.

In = SQRT((Ia*Ia+Ib*Ib+Ic*Ic)-(Ia*Ib+Ib*Ic+Ic*Ia))

So in your example:
In=SQRT((10*10+5*5+15*15)-(10*5+5*15+15*10))