import arcpy

# Set the input line feature class
fc = "C:/Temp/MyLineFeatureClass.gdb/MyLineFeatureClass"

# Set the tolerance for duplicate vertices
tolerance = 0.001

# Create a new cursor to iterate through the features in the input line feature class
cursor = arcpy.da.SearchCursor(fc, ["SHAPE@", "OBJECTID"])

# Create a new empty list to store the XY coordinates of the duplicate vertices
duplicate_vertices = []

# Iterate through the features in the input line feature class
for row in cursor:

    # Get the shape of the feature
    shape = row[0]

    # Get the number of vertices in the shape
    num_vertices = shape.partCount

    # Iterate through the vertices in the shape
    for i in range(num_vertices - 1):

        # Get the XY coordinates of the current vertex
        current_vertex = shape.getPart(i).centroid

        # Get the XY coordinates of the next vertex
        next_vertex = shape.getPart(i + 1).centroid

        # Calculate the distance between the current vertex and the next vertex
        distance = current_vertex.distanceTo(next_vertex)

        # If the distance is less than the tolerance, then the vertices are considered duplicates
        if distance < tolerance:

            # Add the XY coordinates of the duplicate vertex to the list
            duplicate_vertices.append(current_vertex)

# Close the cursor
cursor.close()

# Create a new empty list to store the XY coordinates of the duplicate vertices in string format
duplicate_vertices_string = []

# Iterate through the duplicate vertices and convert them to string format
for vertex in duplicate_vertices:

    # Convert the vertex to string format
    vertex_string = str(vertex.X) + "," + str(vertex.Y)

    # Add the vertex string to the list
    duplicate_vertices_string.append(vertex_string)

# Export the XY coordinates of the duplicate vertices to a CSV file
csv_file = open("C:/Temp/duplicate_vertices.csv", "w")
csv_writer = csv.writer(csv_file)

# Write the header row to the CSV file
csv_writer.writerow(["X", "Y"])

# Write the XY coordinates of the duplicate vertices to the CSV file
for vertex_string in duplicate_vertices_string:

    # Write the vertex string to the CSV file
    csv_writer.writerow([vertex_string])

# Close the CSV file
csv_file.close()