how to uv map a sphere?

Hello, i've been trying to create a procedural sphere but with variable "longitudes" and "latitudes" and making it smooth. its all perfect but the uv mapping. i have done an algorithm but i have no idea what is wrong nor how to find out. here is the script:

 void CreateUV () 
     {
 
         float xDist = 1 / longitude;
         float ang = 180 / (latitude - 1);
         float count = 0;
         for (int y = 0; y < latitude; y++)
         {
             float yDist = Mathf.Cos(ang * y * Mathf.Deg2Rad);
             for (int x = 0; x < longitude; x++)
             {
                 if (y == 0 || y == latitude - 1){
                     uvs.Add(new Vector2(xDist * x + xDist / 2, yDist * y));
                 }
                 else
                 {
                     uvs.Add(new Vector2(xDist * x, yDist * y));
                 }
 
                 count ++;
             }
         }
 

what i was going for is an unwrap like this one:

*if it does not appear ill try and describe it at the end.

in paper seems like it should work though my textures appear as a solid color. also this is the first time i try and map uvs, so here is how i think it works:

the verts are asigned a vector 2 value from (0, 0) to (1, 1) according to their position in a texture.

i would realy apreciate any suggestion or idea. thanks a lot to you all.

*if the image does not appear it basicaly looks like this

         0     1     2  ...
       /   \  /  \ /   \
     3-------4----5-----6 ...
     |       |    |     |
     |       |    |     |
     7-------8----9----10 ...
     |       |    |     |
     |       |    |     |
     11------12---13----14
       \    /  \ /  \   /
         15     16    17

that is the best i could.