My solutions based on the wrong assumption that the view angle has only one maximum on abscissa axis (and with some tricks regarding to range of search or partition method in ternary search) pass all tests. Seems that more tests needed.
Yes. It's zero at negative infinity, increases when moving to positive infinity and than decreases to zero at the point of intersection of the line containing billboard segment and the abscissa axis (assuming the segment itself doesn't intersect the axis). If we continue to move the view point to the positive infinity, the angle increases and decreases again.
Now I understand what you meen. I searched maximum on the segment between point of intersection of board with abscissa axis and positive or negative infinity. I considered only this segment and was surprised that there can be more than one maximum on it.