How to make subscript follow the large angle instead of aligning with the bottom line of the equation?

Question

I have the following latex code and I don't know how to align the subscript f with the \rangle.

Making the langle and rangle bigger is also possible but I didn't find a solution. I've tried to use sbox0 but I failed.

My original code is :

\begin{equation}
\begin{aligned}
\left\langle\frac{a}
{
\begin{aligned}
b\\
c\\
d\\
e\\
\end{aligned}
}
\dots\right \rangle_{f}
\end{aligned}
\end{equation}

The result of XeLaTeX compilation is as follows:

How can I make the f following the \rangle?

Following instructions in big angle brackets and using sbox0, I changed my code as follows:

\begin{equation}
\begin{aligned}
\sbox0{
\frac{a}
{
\begin{aligned}
b\\
c\\
d\\
e\\
\end{aligned}
}
\dots}
\mathopen{\resizebox{1.2\width}{\ht0}{$\Bigg\langle$}}
\usebox{0}
\mathclose{\resizebox{1.2\width}{\ht0}{$\Bigg\rangle$}}
\end{aligned}
\end{equation}

And obviously I failed.

Answer 1

Something like this?

Observe that I've gotten rid of both aligned environments. The outer one doesn't appear to be doing anything useful at all, and the inner one is best replaced with a matrix environment.

\documentclass{article}
\usepackage{amsmath}
\begin{document}
[
\left\langle
\frac{a}{ \begin{matrix} b\ c\ d\ e\ \end{matrix}} 
\cdots
\right\rangle 
{\vphantom{\frac{a}{b}}}_{!!f} % '!!' is used to "snug up" the subscript term
]
\end{document}