This UDF should do what you want.
Try the formula =RemoveBrackets(C1)
Function RemoveBrackets(aString As String) As String
    Dim i As Long, Snippets As Variant
    aString = Application.Substitute(aString, "<", ">")
    Snippets = Split(aString, ">")
    For i = 0 To UBound(Snippets) Step 2
        RemoveBrackets = RemoveBrackets & Snippets(i)
    Next i
End Function