Dear Wolfram Community,

In my ongoing exploration of integrating AI technology with analytical computing, I've been employing the GPT-4 Vision Preview for image recognition coupled with the Wolfram Language to recreate a specific illustration.

The image in question depicts a vector, \hat{n}, in a three-dimensional spherical coordinate system, identified by the angles \alpha (azimuthal) and \beta (polar).

With the help of GPT-4 Vision Preview, I was able to generate an initial Wolfram Language code for the task. However, the current output does not accurately reflect the original image and lacks in replicating some intricate graphical details.

Here's the code snippet generated by the GPT-4 Vision Preview using Wolfram language:

(* Create the vector *)
vector = Graphics3D[{Arrowheads[0.03], Arrow[{{0, 0, 0}, {1, 1, 1}}]}, 
  Boxed -> False];

(* Label the axes *)
axesLabels = Graphics3D[{
   Text[Style["x", 12, Italic], {1.2, 0, 0}], 
   Text[Style["y", 12, Italic], {0, 1.2, 0}], 
   Text[Style["z", 12, Italic], {0, 0, 1.2}]
   }];

(* Combine the vector and the axes labels *)
Show[vector, axesLabels, 
 PlotRange -> {{-0.5, 1.2}, {-0.5, 1.2}, {-0.5, 1.2}}, 
 Axes -> True, AxesOrigin -> {0, 0, 0}, ImageSize -> Large]

Though the above code effectively renders a basic 3D plot with a vector and labelled axes, it falls short when it comes to capturing intricate details such as dashed lines, the angles \alpha and \beta, and the curved arrows around the axes in the original illustration.

I, therefore, turn to your expert knowledge to understand how this code can be refined. How can I maximally leverage the GPT-4 Vision Preview in conjunction with Wolfram Language to accurately replicate the image, encompassing all its details?

The original illustration which I want to reproduce is as follows:

I greatly appreciate your guidance and look forward to your insights.

Best regards,
Zhao