In a physics laboratory experiment, a coil with $240$ turns enclosing an area of $12\mathrm{.}7$ cm$2$cm$2$ is rotated during the time interval $4\mathrm{.}20102$ ss from a position in which its plane is perpendicular to Earth's magnetic field to one in which its plane is parallel to the field. The magnitude of Earth's magnetic field at the lab location is $5\mathrm{.}70105$ TT $.$ What is the magnitude of the magnetic flux $($initial$$initial$)$ through the coil before it is rotated?