Correct the size of < > in math mode?

Question

I am using \left< and \right> to indicate the average in an equation. Unfortunately it looks quite strange in the following example, as the automatic size estimation is different for both sides of the equation. Is there any way to fix this, so that it looks "correct"?

\documentclass{standalone}

\begin{document}

$\left< \Delta \eta \right>^2 \ll \left< \eta^2 \right>$

\end{document}

At the moment the output is as follows with clearly visible difference in size of the parentheses.

Answer 1

Like this?

Code

\documentclass[border=2pt]{standalone}

\begin{document}

$\left< \Delta \eta\vphantom{^2} \right>^2 \ll \left< \eta^2 \right>$

\end{document}

Output

Or like that?

Code

\documentclass[border=2pt]{standalone}

\begin{document}

$\left< \Delta \eta \right>^2 \ll \left< \eta\smash{^2} \right>$

\end{document}

Output

Or with fixed-size delimeters

Code A

\documentclass[border=2pt]{standalone}

\begin{document}

$\bigl< \Delta \eta \bigr>^2 \ll \bigl< \eta^2 \bigr>$

\end{document}

Output A

Code B

\documentclass[border=2pt]{standalone}

\begin{document}

$\langle \Delta \eta \rangle^2 \ll \langle \eta^2 \rangle$

\end{document}

Output