How to fix my antlion modmic 4 cable that I just cut in two pieces?

[koutso.xtapodaki]

I bought it a few months ago and I am willing to try to fix it before buying a new one since it's expensive.
It will be my first time soldering and rejoining wires so I would like a detailed step by step guide.

The official site says its a 2.5 mm diameter, coaxial shielding wire.

In the following picture I separated all the wires and twisted them to get a clear view on what I got to deal with.
Green wire is the microphone, the copper wire was covering the green one and there is a white thread thingy that I suppose I should just ignore.
How to proceed and what tools do I need to buy?

Thanks!

 

[hang-the-9]

Seems pretty simple, strip off the ends of the wires, wrap them around the other end, tape up the whole thing with some electrical tape.