Calculate target range on circle Three.js

I have a Math problem I'm struggling with.

I have a particular radian I want to point the camera at (camera.rotation.y). I want to tell the user if they need to pan left or right to get to that radian, with a tolerance of PI/4.

I've normalised the pan number by getting the camera + dolly rotation

function getCurrentPan(){
    return dolly.rotation.y + camera.rotation.y > 0
        ? (dolly.rotation.y + camera.rotation.y)%Math.PI
        : ((dolly.rotation.y + camera.rotation.y)%Math.PI) + Math.PI;
}

So it's always between 0 and PI.

I'd planned on working out the range which I can check against to see if the user needs to pan left or right to get to that radian. Trying this code:

      point.leftRange = {};
        point.leftRange.min = point.pan - range > 0 ? point.pan - range : Math.PI - point.pan - range;
        point.leftRange.max = point.leftRange.min - Math.PI/2 - range > 0 ? (point.pan - range)%Math.PI : (Math.PI - (point.leftRange.min - Math.PI/2 - range))% Math.PI;

        console.log(point.leftRange);

        point.rightRange = {};
        point.rightRange.min = (point.pan + range) % Math.PI;
        point.rightRange.max = (point.rightRange.min + (Math.PI/2 - range)) % Math.PI;

        console.log(point.rightRange);

Which is giving me something like

point.pan 1.464308692701496
left.min 1.071609611002772
left.max 0.8918857974908487
right.min 1.8570077744002202
right.max 3.0351050194963927

Another approach I've tried is

             var opp = (point.pan - Math.PI/2)%Math.PI;
                opp = opp > 0 ? opp : Math.PI - opp;

                if(getCurrentPan() > point.pan && getCurrentPan() < opp)
                     console.log('greater');
                else if(getCurrentPan() < point.pan && getCurrentPan() > opp)
                     console.log('less');

Which again won't take into account if the pan is like 0.5 and left range is 3 etc (other side of PI).

Sorry I'm not explaining this well but if anyone can point me the right direction I'd appreciate it!

Solution

This is overengineered. if you want to figure out whether a target is to the left or right of the camera, you do this:

d = camera.getworlddirection();
diff = target.position - camera.position;
theta = atan2(diff.x,diff.z) - atan2(d.x,d.z);

this is the angle between where your camera is looking vs where the object is in relation to the camera.

so:

if(abs(theta) < someThreshold){
  if(theta > 0){
    //its to the right
  }
  else{
   //its to the left
  }
}