There is a photon traveling in the \(xy\)-plane. At \(t = 0\), it is positioned at \((x,y) = \left(-\frac{3}{5} ,\frac{3}{10}\right)\) and it has a velocity \((v_x,v_y) = \left(\frac{1}{2},\frac{\sqrt{3}}{2}\right)\).

The photon is surrounded by a circular mirror of unit radius which is centered on the origin. There is no mirrored surface within the angle range \((-5^{\circ} \leq \theta \leq 5^{\circ}) \), where \(\theta\) is measured with respect to the \(+x\) axis.

At what time does the photon exit the region enclosed by the circular mirror (to 1 decimal place)?

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