It's not trivial. If "Layer 1" is your auto-oriented layer, this expression should give the orientation values (apply it to another layer's orientation property):

L = thisComp.layer("Layer 1");

s = L.scale/100;

u = L.toWorldVec([s[0],0,0]);

v = L.toWorldVec([0,s[1],0]);

w = L.toWorldVec([0,0,s[2]]);

sinb = clamp(w[0],-1,1);

b = Math.asin(sinb/thisComp.pixelAspect);

cosb = Math.cos(b);

if (Math.abs(cosb) > .0005){

c = -Math.atan2(v[0],u[0]);

a = -Math.atan2(w[1],w[2]);

}else{

a = Math.atan2(u[1],v[1]);

c = 0;

}

[radiansToDegrees(a),radiansToDegrees(b),radiansToDegrees(c)]

Dan