Sharing Owin Cookie Authentication and legacy Form

Question

In our company, we have a large base of application built with Asp.net Web Forms 4.0 that use forms authentication as a single-sign-on authentication. Configured something like this:

<machineKey decryptionKey="..." validationKey="..." />
<authentication mode="Forms">
    <forms cookieless="UseCookies" loginUrl="/url/to/login" />
</authentication>

Last times we are working on some projects that use Owin Cookie authentication. According to the searches I did, both methods are not compatible. However I found this post OWIN Self-Host CookieAuthentication & Legacy .NET 4.0 Application / FormsAuthenticationTicket in which I could have a possibility to get both of them working together, but I can't get entire code working very well. In fact I don't know how to develop the remainder codes.

I would ask you if anybody have some solution to this issue or a more simple way to do this?

I need to tell you I have no very much knowledge about the details of Microsoft Implementation of Forms Authentication.