How can I release the GIL before calling an embedded C function?

Question

I have the following Cython code:

cdef public int CythonfunC():
    with nogil:
        embeddedCFunction()

cdef extern from *:
r"""
#include <wchar.h>
#include <Python.h>
#include "cfunctions.h";
#include <tchar.h>
#include <windows.h>

int embeddedCFunction(){
    //do stuff that don't require GIL
    return 0;
}
PyObject *OtherFunctions(){

    return PyObjectX;
}
"""
int embeddedCFunction()

The above code throws the following error: Calling gil-requiring function not allowed without gil. As suggested by some answers, I tried things such as with nogil except:, but I was not successful.

How do I release the GIL before calling embeddedCFunction?