Get angle (position on sphere) from X,Y (U,V)

I have a coordinate in my UV pixel space (detected eye position in video texture) that I display on a sphere, what is the right way to find that pixel location on my sphere (I want to rotate my sphere accordingly so that the point will face certain axis)

I’ve tried some code I found online to find the position of the eye on the sphere -

function convert2d3d(r1, r2, x, y) {
   // r1 - texture size ?
   // r2 - sphere size
   // x,y - position I want to reach on the sphere

   let z = -1 + 2 * x / r1;
   let phi = 2 * Math.PI * y / r1;
   let theta = Math.asin(z);
   return {
      x: r2 * Math.cos(theta) * Math.cos(phi),
      y: r2 * Math.cos(theta) * Math.sin(phi),
      z: r2 * z,

I’m attempting - find detected eye position on sphere and then rotate the sphere according to angle found


might be helpful three.js examples