Removing right margin in Verse environment

I’m using the verse environment to cite verses with long lines (that go through the next line), but because I added margins on the left a weird right margin is also added. This is how it looks:

I want the poem to be aligned with the text on the right margin, but everything that i’m trying don’t work… This is my MWE:

documentclass[a4paper,twoside]{book}
usepackage[margin=1.5cm,top=1.5cm,bottom=2cm]{geometry}
usepackage{setspace}

begin{document}
    Large
    Random text just because
    setlength{leftmargini}{4cm}
    begin{verse}
        large
        singlespacing 
        The quick brown fox jumps over the lazy dog and the five boxing wizards jump quickly.
        second verse 
        third verse
    end{verse}
    
    
end{document}

% verseprob.tex  SE 565347

documentclass[a4paper,twoside]{book}
usepackage[margin=1.5cm,top=1.5cm,bottom=2cm]{geometry}
usepackage{setspace}
usepackage{verse}

begin{document}
    Large
    Random text just because
%    setlength{leftmargini}{4cm}
settowidth{versewidth}{The quick brown fox jumps over}% the lazy dog}% and the five}

    begin{verse}[versewidth]
        large
        singlespacing 
        The quick brown fox jumps over the lazy dog and the five boxing wizards jump quickly.
        second verse 
        third verse
    end{verse}
    
end{document}