Installing pzmq with Cygwin

For two days I have been struggling to install pyzmq and I am really not sure what the issue is.

The error message I receive after:

pip install pyzmq

is:

 error: command 'gcc' failed with exit status 1

I have gcc installed.

which gcc
/usr/bin/gcc

Python is installed at the same location. I am really struggling to find a solution.

Edit: Adding to the output from the error, here is the output that describes the error further:

 bundled/zeromq/src/signaler.cpp:62:25: fatal error: sys/eventfd.h: No  such file or directory
  #include <sys/eventfd.h>
                         ^
compilation terminated.
error: command 'gcc' failed with exit status 1

----------------------------------------
Command "/usr/bin/python -c "import setuptools, tokenize;__file__='/tmp/pip- build-INbMj2/pyzmq/setup.py';exec(compile(getattr(tokenize, 'open', open)(__file__).read().replace('\r\n', '\n'), 
__file__, 'exec'))" install --record /tmp/pip-n8hQ_h-record/install-record.txt --single-version-externally-managed --compile" failed with error code 1 in /tmp/pip-build-INbMj2/pyzmq