How to replace certain Greek letters in mtpro2 with their counterparts from newtxmath

Question

I use mtpro2 package in my article for writing math and Times Roman for text. The question is how to use certain Greek letters (like \gamma which I see better in newtxmath) from newtxmath instead of those in mtpro2. Here is a MWE:

\documentclass{article}
\usepackage[T1]{fontenc}
\renewcommand{\rmdefault}{ptm}
\usepackage{amsmath,amsfonts}
\usepackage[zswash,lite]{mtpro2}
\usepackage{bm}

\begin{document}

Law of Quadratic Reciprocity:

Some text goes here ...
\begin{equation}
f(z) = 50\sigma \times E_0 e^{-\gamma x} \cos(\omega t-\beta z) \mathbf{a}_x \quad \mathbf{A} + \Gamma
\end{equation}
\end{document}

UPDATE:

For gamma, the problem was solved with the the answer by @egreg below, but for Gamma it wasn't. I tried the following workaround:

\DeclareSymbolFont{newtxletters}{OML}{ntxmi}{m}{it}
\SetSymbolFont{newtxletters}{bold}{OML}{ntxmi}{b}{it}
\DeclareMathSymbol{\Gamma}{\mathord}{newtxletters}{0}

but it gave me the italic version of Gamma. I know that mtpro2 and newtxmath have different (and incompatible) output encodings, but there must be some workaround. Here is my current code:

\documentclass[12pt,a4paper]{article}
\usepackage[T1]{fontenc}
\usepackage{tgtermes}
\usepackage{amsmath,amssymb,amsfonts}
\usepackage[lite]{mtpro2}
\usepackage{bm}

\begin{document}

\[
\gamma \ \bm{\gamma} \ \Gamma \ \bm{\Gamma} 
\]

\end{document}

Which outputs this:

But the required is this:

Thank you.

Answer 1

Define a new symbol font using the font of newtxmath and tell TeX to take \gamma from it.

\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage{tgtermes}
\usepackage{amsmath,amsfonts}
\usepackage[zswash,lite]{mtpro2}
\usepackage{bm}

\DeclareSymbolFont{newtxletters}{OML}{ntxmi}{m}{it}
\SetSymbolFont{newtxletters}{bold}{OML}{ntxmi}{b}{it}
\DeclareMathSymbol{\gamma}{\mathord}{newtxletters}{13}

\begin{document}

Law of Quadratic Reciprocity: $\gamma\ne\beta$
\begin{equation}
f(z) = 50\sigma \times E_0 e^{-\gamma x} \cos(\omega t-\beta z) \mathbf{a}_x \quad \mathbf{A} + \Gamma
\end{equation}
\end{document}

Here's the same without the change.