The joint density of the total winding and the radius of a planar Brownian motion is calculated, by solving the associated backward equation. An explicit expression for the distribution of the hitting time of an angular barrier is shown; in particular, the behavior of the tail of the distribution is determined.
"A Note on Planar Brownian Motion." Ann. Probab. 20 (3) 1498 - 1503, July, 1992. https://doi.org/10.1214/aop/1176989703