*I don't claim to have made this puzzle, nor do I have a solution.*

The is a circle of radius 3 meters with an ant in the centre. The ant picks a direction randomly, all angles have an equal probability. It walks in this direction for 1 meter before fogetting where it was going and chosing another direction randomly. This could go on forever, but on average how many meters has the ant travelled before it exists the circle?

Computers are allowed, but I do want to see a mathematical solution.