Augmented chords are interesting and although they sound a bit harsh, when used they can add colour to music. I like the way they sound although some times they are difficult to play. The key with augmented chords (or every chord to my opinion) is to understand what they are, how they are constructed, i.e. the music theory behind augmented chords, but also to learn how to play them using one of the usual fingerings.
If we now focus on the C# augmented chord, we will see that this chord in root position consists of C#-E#-G## and is named C# aug, in first inversion it consists of E#-G##-C# and is called C#/E# aug and is second inversion consists of G##-C#-E# and is called C#/G## aug.
Similarly, a Db augmented chord in root position consists of Db-F-A and is named Db aug, in first inversion it consists of F-A-Db and is called Db/F aug, and is second inversion consists of A-Db-F and is called Db/A aug.
Lets now dive deeper to see details of construction and more importantly how to play it on the mandolin.