Bouncing Photon (Part 2)

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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