Suppose a light source is positioned in R at the origin (0, 0). Smooth mirrors are positioned along the lines y = 0 and y = 2 from x = 0 to x = 10. The light source is then oriented so that the beam of light emanating from it makes an angle, chosen uniformly and at random, of between 15 and 75 with the positive x-axis. The beam is then allowed to reflect back and forth between the two mirrors until it "exits the tunnel", that is, it crosses the line x = 10. If the expected distance that the beam of light travels from its source until it exits the tunnel 10 can be expressed as In(a+bc), where a, b, c are positive integers with c square-free, then find a + b + c. T