Add Box to multiline-expression which is part of aligned-equation?

Question

I want to add a box (black color) to encapsulate the last two lines of this triple-line-aligned expression.

As you can see, the current solution inspired by this post is not perfect because it misses some topmost components.

Note that the target is a part of the aligned-expression so the general commends like boxed or empheq may not work.

\newcommand{\pstrut}[1]{\vrule height0pt depth0pt width0pt #1 \fboxsep}
\newcommand*\bmarkeq{\stepcounter{markeq}%
  \tikz[remember picture]\node(startframe-\themarkeq){\pstrut{height}};%
  \kern\fboxsep}
\newcommand*\emarkeq{\kern\fboxsep
  \begin{tikzpicture}[remember picture,overlay]
    \node (endframe-\themarkeq){\pstrut{depth}};
    \draw[,black,opacity=0.8] (startframe-\themarkeq.north) 
      rectangle (endframe-\themarkeq.south);
  \end{tikzpicture}%
}
\begin{align}
    \mathrm{L}{c}(\theta) 
    = &\sum{i=1}^{m} \ln p\left(x_{i}, z_{i} ; \theta\right) \
    = \bmarkeq &\sum_{i=1}^{m}\left(z_{i}\left[\ln (\pi)+x_{i} \ln \left(p_{r}\right)+\left(1-x_{i}\right) \ln \left(1-p_{r}\right)\right] \
    &+ \left(1-z_{i}\right)\left[\ln (1-\pi)+x_{i} \ln \left(p_{b}\right)+\left(1-x_{i}\right) \ln \left(1-p_{b}\right)\right]\right) \emarkeq
\end{align}

Answer 1

You don't need TiKZ to do that: amsmath has the \boxed command and mathtools adds the \Aboxed command, which may include the alignment points. Here are two suggestions to do that:

\documentclass{article}
\usepackage{mathtools}
\begin{document}
\begin{align}
    \mathrm{L}{c}(\theta)
    &=\sum{i=1}^{m} \ln p(x_{i}, z_{i} ; \theta) \
   & =\boxed{\begin{aligned}[t] &\sum_{i=1}^{m}\bigl(z_{i}\bigl[\ln (\pi)+x_{i} \ln (p_{r})+(1-x_{i}) \ln(1-p_{r})\bigr]\
   &+(1-z_{i})\bigl[\ln (1-\pi)+x_{i} \ln(p_{b})+(1-x_{i}) \ln(1-p_{b})\bigr]\bigr)\end{aligned}}
\end{align}
\begin{align}
    \mathrm{L}{c}(\theta)
    &=\sum{i=1}^{m} \ln p(x_{i}, z_{i} ; \theta) \
\Aboxed{& ={\begin{aligned}[t]&\sum_{i=1}^{m}\bigl(z_{i}\bigl[\ln (\pi)+x_{i} \ln (p_{r})+(1-x_{i}) \ln(1-p_{r})\bigr]\
   &+(1-z_{i})\bigl[\ln (1-\pi)+x_{i} \ln(p_{b})+(1-x_{i}) \ln(1-p_{b})\bigr]\bigr)\end{aligned}}}
\end{align}
\end{document}