The Piper Cherokee $($a light, single$-$engine general aviation aircraft$)$ has a wing area of $170$ ft$2$ and a wing span of $32$ ft$.$ Its maximum gross weight is $2450$ lb$.$ The wing uses an NACA $65-415$ airfoil, which has a lift slope of $0\mathrm{.}1033$ degree$1$ and L$=0=3.$ Assume $=0\mathrm{.}12.$ If the airplane is cruising at $119\mathrm{.}0$ mi$/$h at standard sea level at its maximum gross weight and is in straight$-$and$-$level flight, calculate the geometric angle of attack of the wing. $($Round the final answer to three decimal places.$)$