import numpy as np
from numpy.linalg import norm

def normalize_landmarks(landmarks):
    """
    Normalize the hand landmarks.
    
    Parameters:
        landmarks (numpy.ndarray): Array of hand landmarks.

    Returns:
        numpy.ndarray: Normalized landmarks.
    """
    center = np.mean(landmarks, axis=0)
    landmarks_centered = landmarks - center
    std_dev = np.std(landmarks_centered, axis=0)
    landmarks_normalized = landmarks_centered / std_dev
    return np.nan_to_num(landmarks_normalized)

def calculate_angles(landmarks):
    """
    Calculate angles between hand landmarks.
    
    Parameters:
        landmarks (numpy.ndarray): Array of hand landmarks.

    Returns:
        list: List of calculated angles.
    """
    angles = []
    for i in range(20):
        for j in range(i + 1, 21):
            vector = landmarks[j] - landmarks[i]
            angle_x = np.arccos(np.clip(vector[0] / norm(vector), -1.0, 1.0))
            angle_y = np.arccos(np.clip(vector[1] / norm(vector), -1.0, 1.0))
            angles.extend([angle_x, angle_y])
    return angles