Yes, there is.
You will need to work with the path.curves representation of a path as opposed to the path.segments.
The Curve object has a function called curve.getTangent(parameter) which returns the tangent in any given point of the curve as a point / vector. The position is defined by the bezier curve parameter that is a value between 0 and 1.
To find the curve / parameter pair at a given length of a path you can use path.getPositionWithLength(length) which returns a HitResult object that points to the curve and the bezier parameter at the given position. You then can use this to find the tangent in that point, and from this the angle. So to get the angle of the path at a third of its length, you would do this:
var pos = path.getPositionWithLength(path.length / 3);
var tangent = pos.curve.getTangent(pos.parameter);
var angle = tangent.angle;
That should do it!