NASA's Hubble Space Telescope and scientists running simulations have predicted a collision between the Milky Way and Andromeda galaxies in about 4 billion years. Although the two galaxies will collide, scientists believe the sun and Earth are not in danger because space between stars is so great, there won't be any cataclysmic collisions. Scientists do believe our solar system will be flung further away from the galactic center than it is now. Hopefully, humans will still be around to witness the event. Our sun is supposed to become a red giant star by then, so there is a distinct possibility the Earth will be destroyed before this clash of the titans in our local universe.
I'm skeptical about the exact figure of 3.6 billion years being the exact figure, but I do believe our two galaxies are on a collision path. I've heard estimates ranging from 100,00 to 10 billion years as the date for the collision of the Milky Way and Andromeda galaxies. Most scientists agree though, that it will happen. The better bet to take in Vegas, rather than under or over 3.6 billion years, is whether or not they will collide. Put your bankroll on these two galaxies colliding!