two rotation motion combined

one with Euler angles the other with quaternion slerp can NOT apply to the same group

HTML

<div id="info">Two-Layer Orientation Interpolation</div>
<script src="http://cdnjs.cloudflare.com/ajax/libs/three.js/r70/three.min.js"></script>
<script src="https://dl.dropboxusercontent.com/u/3587259/Code/Threejs/OrbitControls.js">


</script>

CSS

#info {
  position: absolute;
  top: 0px;
  width: 100%;
  padding: 10px;
  text-align: center;
  color: #ffff00
}

body {
  overflow: hidden;
}

JavaScript

var camera, scene, renderer, mesh, controls;
var group, group2;
var quat1, quat2, qm;

init();
animate();

function init() {
  scene = new THREE.Scene();

  camera = new THREE.PerspectiveCamera(50, window.innerWidth / window.innerHeight, 1, 1000);
  camera.position.z = 500;
  scene.add(camera);

 	var light = new THREE.PointLight(0xffffff);
  light.position.set(100, 300, 200);
  scene.add(light);

  var gridXZ = new THREE.GridHelper(100, 10);
  gridXZ.setColors(new THREE.Color(0xff0000), new THREE.Color(0xffffff));
  scene.add(gridXZ);

  renderer = new THREE.WebGLRenderer();
  renderer.setSize(window.innerWidth, window.innerHeight);
  renderer.setClearColor(0x888888);

  controls = new THREE.OrbitControls(camera, renderer.domElement);

  document.body.appendChild(renderer.domElement);
  window.addEventListener('resize', onWindowResize, false);

	////////////////////////////////////////////////////////////////////
  var geometry = new THREE.BoxGeometry(200, 200, 1200);
  var material = new THREE.MeshLambertMaterial();

  mesh = new THREE.Mesh(geometry, material);
  mesh.position.set(0, 0, 60);
  group = new THREE.Object3D();  // lower end is at origin, pointing +Z
  group.add(mesh);
  group2 = new THREE.Object3D();
  group2.add(group);
  scene.add(group2);

  // setting keyframes
  quat1 = new THREE.Quaternion();
  quat1.setFromAxisAngle(new THREE.Vector3(0, 1, 0), Math.PI / 6);
  quat2 = new THREE.Quaternion();
  quat2.setFromAxisAngle(new THREE.Vector3(0, 1, 0), -Math.PI / 3);
  qm = new THREE.Quaternion(); // quat for slerp
}

function onWindowResize() {
  camera.aspect = window.innerWidth / window.innerHeight;
  camera.updateProjectionMatrix();
  renderer.setSize(window.innerWidth, window.innerHeight);
}

function animate() {
	animate.tt = animate.tt || 0;
  animate.sign2 = animate.sign2 || 1;
  if (animate.tt > 1 || animate.tt < 0)
  	animate.sign2 *= -1;
 	animate.tt += 0.01*animate.sign2;
 
	// quaterion slerp : tt: [0,1]
  THREE.Quaternion.slerp(quat1,...