Beamer (Boadilla theme): Color of itemize subitems inside blocks

Question

When using the "Boadilla" theme in the beamer package, I noticed that the bullets of subitems in the itemize environment have different colors inside block environments than outside. The problem is that the color is almost the same as the background, so the individual bullets are barely visible.

Is there a way to change the subitem bullet color to the same color used outside of blocks?

Here is an example of the problem:

\documentclass{beamer}
\usetheme{Boadilla}

\begin{document}

\begin{frame}
    \begin{block}{block}
        \begin{itemize}
            \item item 1
            \item item 2
            \begin{itemize}
                \item subitem 1
                \item subitem 2
                \begin{itemize}
                    \item subsubitem
                \end{itemize}
            \end{itemize}
        \end{itemize}
    \end{block}

    \begin{itemize}
        \item item 1
        \item item 2
        \begin{itemize}
            \item subitem 1
            \item subitem 2
            \begin{itemize}
                \item subsubitem
            \end{itemize}
        \end{itemize}
    \end{itemize}
\end{frame}

\end{document}

Answer 1

I don't understand very well how does it work, but a fast solution is to add these lines to the preamble or inside a group where you wish to get that result.

\colorlet{custom}{beamerstructure}
\setbeamertemplate{itemize subitem}{\tiny\raise1.5pt\hbox{\color{custom}$\blacktriangleright$}}
\setbeamertemplate{itemize subsubitem}{\tiny\raise1.5pt\hbox{\color{custom}$\bigstar$}}

I tried to patch the Boadilla theme definitions.

Full Code

\documentclass{beamer}
\usetheme{Boadilla}

\colorlet{custom}{beamerstructure}
\setbeamertemplate{itemize subitem}{\tiny\raise1.5pt\hbox{\color{custom}$\blacktriangleright$}}
\setbeamertemplate{itemize subsubitem}{\tiny\raise1.5pt\hbox{\color{custom}$\bigstar$}}
\begin{document}

\begin{frame}
    \begin{block}{block}
        \begin{itemize}
            \item item 1
            \item item 2
            \begin{itemize}
                \item subitem 1
                \item subitem 2
                \begin{itemize}
                    \item subsubitem
                \end{itemize}
            \end{itemize}
        \end{itemize}
    \end{block}

    \begin{itemize}
        \item item 1
        \item item 2
        \begin{itemize}
            \item subitem 1
            \item subitem 2
            \begin{itemize}
                \item subsubitem
            \end{itemize}
        \end{itemize}
    \end{itemize}
\end{frame}

\end{document}

Result