GLSL calculating normal on a sphere mesh in vertex shader using noise function by sampling is producing strange graphical errors

Question

I'm trying to calculate the normals on surface of a sphere in the vertex shader because I defer my noise calculation to the vertex shader. The normal results are good when my theta (sampling angle) is closer to 1 but for more detailed terrain & a smaller theta my normals become very incorrect. Here's what I mean:

Accurate normals

More detailed noise with a higher theta

Zoomed in onto surface of last image. Red indicates ridges, blue indicates incorrect shadows

The code I use to calculate normals is:

vec3 calcNormal(vec3 pos)
{
    float theta = .1; //The closer this is to zero the less accurate it gets
    vec3 vecTangent = normalize(cross(pos, vec3(1.0, 0.0, 0.0))
        + cross(pos, vec3(0.0, 1.0, 0.0)));
    vec3 vecBitangent = normalize(cross(vecTangent, pos));
    vec3 ptTangentSample = getPos(pos + theta * normalize(vecTangent));
    vec3 ptBitangentSample = getPos(pos + theta * normalize(vecBitangent));

    return normalize(cross(ptTangentSample - pos, ptBitangentSample - pos));
}

I call calcNormal with

calcNormal(getPos(position))

where getPos is the 3D noise function that takes and returns a vec3 and position is the original position on the sphere.

Answer 1

Thanks to @NicoSchertler the correct version of calcNormal is

vec3 calcNormal(vec3 pos)
{
    float theta = .00001; 
    vec3 vecTangent = normalize(cross(pos, vec3(1.0, 0.0, 0.0))
     + cross(pos, vec3(0.0, 1.0, 0.0)));
    vec3 vecBitangent = normalize(cross(vecTangent, pos));
    vec3 ptTangentSample = getPos(normalize(pos + theta * normalize(vecTangent)));
    vec3 ptBitangentSample = getPos(normalize(pos + theta * normalize(vecBitangent)));

     return normalize(cross(ptTangentSample - pos, ptBitangentSample - pos));
  }