How can I set the camera angle to something like the isometric projection?
To get an isometric view, you can use an OrthographicCamera. You then need to set the camera's orientation properly. There are two ways to do that:
Method 1 - use camera.lookAt()
const aspect = window.innerWidth / window.innerHeight;
const d = 20;
camera = new THREE.OrthographicCamera( - d * aspect, d * aspect, d, - d, 1, 1000 );
camera.position.set( 20, 20, 20 ); // all components equal
camera.lookAt( scene.position ); // or the origin
method 2 - set the x-component of camera.rotation
camera.position.set( 20, 20, 20 );
camera.rotation.order = 'YXZ';
camera.rotation.y = - Math.PI / 4;
camera.rotation.x = Math.atan( - 1 / Math.sqrt( 2 ) );

EDIT: updated fiddle: https://jsfiddle.net/vkjew52q/
three.js r.146
you need to use orbit and track controls , like in here :
http://codepen.io/nireno/pen/cAoGI
Edit:
also you may consider using ortho camera this post here may help you :
Three.js - Orthographic camera
an example can be seen here :
http://threejs.org/examples/canvas_camera_orthographic.html
and here is a link (udacity) explaining the use:
https://www.udacity.com/course/viewer#!/c-cs291/l-158750187/m-169414761
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