Shader that transforms a mercator projection to equirectangular?
This question and its answer, actually answer my question. I had to read its answer carefully and find my mistake.

Now my fragment shader look like this:

const GLchar* fragmentSource = R"glsl(
    #version 330 core

    in vec2 TexCoord;

    uniform sampler2D ourTexture;

    #define PI       3.141592653589793238462f
    #define TWO_PI   6.283185307179586476924f
    #define PI4      0.7853981633974483096155f

    void main(){
        float lat = (TexCoord.y - 0.5f) * PI;
        if(lat &gt;= -1.48442222974871 &amp;&amp; lat &lt;= 1.48442222974871){
            float y = log(tan(PI4 + (lat / 2.0)));
            y = (y + PI) / TWO_PI;
            gl_FragColor = texture(ourTexture, vec2(TexCoord.x, y));
            return;
        }
        gl_FragColor = vec4(1, 1, 1, 0);
    }
)glsl";


And it's works perfectly.