Calculate Z Rotation of a face in Tensorflow.js

Note: This question has NOTHING to do with Three.js, it's only Tensorflow.js and Trigonometry.

I am trying to rotate a 3D object in Three.js by rotating my face. I have used this code by akhirai560 for rotating in X and Y axis.:

function normal(vec) {
  let norm = 0;
  for (const v of vec) {
    norm += v * v;
  }
  return Math.sqrt(norm);
}

function getHeadAnglesCos(keypoints) {
  // Vertical (Y-Axis) Rotation
  const faceVerticalCentralPoint = [
    0,
    (keypoints[10][1] + keypoints[152][1]) * 0.5,
    (keypoints[10][2] + keypoints[152][2]) * 0.5,
  ];
  const verticalAdjacent = keypoints[10][2] - faceVerticalCentralPoint[2];
  const verticalOpposite = keypoints[10][1] - faceVerticalCentralPoint[1];
  const verticalHypotenuse = normal([verticalAdjacent, verticalOpposite]);
  const verticalCos = verticalAdjacent / verticalHypotenuse;

  // Horizontal (X-Axis) Rotation
  const faceHorizontalCentralPoint = [
    (keypoints[226][0] + keypoints[446][0]) * 0.5,
    0,
    (keypoints[226][2] + keypoints[446][2]) * 0.5,
  ];
  const horizontalAdjacent = keypoints[226][2] - faceHorizontalCentralPoint[2];
  const horizontalOpposite = keypoints[226][0] - faceHorizontalCentralPoint[0];
  const horizontalHypotenuse = normal([horizontalAdjacent, horizontalOpposite]);
  const horizontalCos = horizontalAdjacent / horizontalHypotenuse;

  return [horizontalCos, verticalCos];
}

It calculates the rotation by finding the cos of these points (original image source):

I also want to calculate the cos of Z axis rotation. Thanks!

from Calculate Z Rotation of a face in Tensorflow.js