Rotate the ellipse to meet the parabola

The ellipse

$\dfrac{x^2}{7^2}+ \dfrac{y^2}{3^2} = 1$

is shifted to the right such that its left focus becomes at the origin. Then, the ellipse is rotated, about the origin, counter clockwise by an angle $\theta , 0^{\circ} \le \theta \lt 360^{\circ} ,$ so that it becomes tangent to the parabola $y = 5 + \dfrac{1}{16} (x - 12)^2$ . Find the angle of rotation $\theta$ in degrees (choose the smaller of two possible angles), and submit $\lfloor 100 \hspace{4pt} \theta \rfloor$ .