The curves vec$(r{)}_1(t)=($:$8sin(t),10cos(t),e^{4t}$:$)$ and vec$(r{)}_2(t)=($:$3ln(t),10\sqrt[\phantom{2}]{t},t^2$:$)$ intersect at the point $(0,10,1).$

Find the angle of intersection, in radians on the domain $0,$ to two decimal places.