Maximum Number of Visible Points

You are standing at the top of a hill at a fixed position. Around you are several trees, each located at a specific (x, y) coordinate and with a certain height. You want to take a photo that captures as many trees as possible within a single frame. Given your position and the positions of the trees, write an algorithm to determine the maximum number of trees visible within a given viewing angle. Trees that lie in the same direction (same line of sight) should count as one visible tree, since nearer trees block the view of those behind them.