A way to calculate the angle around an axis (make it turn around its head y axis).

AngleAroundAxis.cs

public static float AngleAroundAxis (Vector3 dirA, Vector3 dirB, Vector3 axis) 
{
    // Project A and B onto the plane orthogonal target axis
    dirA = dirA - Vector3.Project (dirA, axis);
    dirB = dirB - Vector3.Project (dirB, axis);
 
    // Find (positive) angle between A and B
    float angle = Vector3.Angle (dirA, dirB);
 
    // Return angle multiplied with 1 or -1
    return angle * (Vector3.Dot (axis, Vector3.Cross (dirA, dirB)) < 0 ? -1 : 1);
}