Unity Shader For 360 Virtual Tour

Question

Currently im creating a virtual tour by wrapping a material of a panorama image onto a sphere and turning it inside out. To do that, i used a shader that i got from another stack overflow, the problem is there's no explanation on how to understand the code and i really need to understand the algorithm on how to turn the material inside out... all i know so far is that its using an algorithm to convert normal coordinates to pole coordinate but i still cant find an example to learn from it.. can anyone tell me how this algorithm works? or how to learn this algorithm and any references? Thank you!

question

Here are the shader code :

Shader "Custom/Equirectangular" {
    Properties {
        _Color ("Main Color", Color) = (1,1,1,1)
        _MainTex ("Diffuse (RGB) Alpha (A)", 2D) = "gray" {}
    }

    SubShader{
        Pass {
            Tags {"LightMode" = "Always"}
            Cull Front

            CGPROGRAM
                #pragma vertex vert
                #pragma fragment frag
                #pragma fragmentoption ARB_precision_hint_fastest
                #pragma glsl
                #pragma target 3.0

                #include "UnityCG.cginc"

                struct appdata {
                   float4 vertex : POSITION;
                   float3 normal : NORMAL;
                };

                struct v2f
                {
                    float4    pos : SV_POSITION;
                    float3    normal : TEXCOORD0;
                };

                v2f vert (appdata v)
                {
                    v2f o;
                    o.pos = UnityObjectToClipPos(v.vertex);
                    o.normal = v.normal;
                    return o;
                }

                sampler2D _MainTex;

                #define PI 3.141592653589793

                inline float2 RadialCoords(float3 a_coords)
                {
                    float3 a_coords_n = normalize(a_coords);
                    float lon = atan2(a_coords_n.z, a_coords_n.x);
                    float lat = acos(a_coords_n.y);
                    float2 sphereCoords = float2(lon, lat) * (1.0 / PI);
                    return float2(1 - (sphereCoords.x * 0.5 + 0.5), 1 - sphereCoords.y);
                }

                float4 frag(v2f IN) : COLOR
                {
                    float2 equiUV = RadialCoords(IN.normal);
                    return tex2D(_MainTex, equiUV);
                }
            ENDCG
        }
    }
    FallBack "VertexLit"

I have tried searching about converting normal coordinates to spherical coordinate but the formula is different from the shader.