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I have made a table that looks as following by using Tabu package:

enter image description here

\documentclass[a4paper, 10pt]{article}

\usepackage{tabu}
\usepackage{multicol}
\usepackage{multirow}
\usepackage{amsmath}

\begin{document}

\begin{center}
{\tabulinesep=1.2mm 
    \begin{tabu}{ |[1.5pt]c|c|c|[1.5pt] }
        \tabucline[1.5pt]{-}
        \textbf{Parameter} & \textbf{Value} & \textbf{Units} \\ \tabucline[1.5pt]{-}
        \multicolumn{3}{ |[1.5pt]c|[1.5pt] }{Nose Parameters} \\ \tabucline[1.5pt]{-}
        $\alpha$ & 10 & Deg \\ \tabucline[1.5pt]{-}
        $[V_{x}(0), V_{y}(0), V_{z}(0)]_{\text{Wind Error}}$ & [0, -6, 0] & m/s \\ \tabucline[1.5pt]{-}
    \end{tabu}}
\end{center}

\end{document} 

How is it possible to make the 3 columns (Parameter/Value/Units) same width according to the widest?

Thank you!

1

like this?

enter image description here

\documentclass{article}
\usepackage{tabu}

\begin{document}
    \begin{center}
    \tabulinesep=1.2mm
\begin{tabu} to 0.6\linewidth { |[1.5pt] *{3}{X[1 c]|}[1.5pt] }
    \tabucline[1.5pt]{-}
\rowfont{\bfseries}
Parameter   &   Value   &   Units       \\ 
    \tabucline[1.5pt]{-}
\multicolumn{3}{ |[1.5pt]c|[1.5pt] }{Nose Parameters} \\ \tabucline[1.5pt]{-}
$\alpha$    & 10        & Deg           \\ 
    \tabucline[1.5pt]{-}
\end{tabu}
    \end{center}
\end{document}

addendum: table with now added row in edited question it is not possible to fit your table with equal width of columns into text width. you should to have firs column wider than second and third:

enter image description here

(red lines indicate text width)

\documentclass[a4paper]{article}
\usepackage{tabu}
\usepackage{amsmath}

\begin{document}
    \begin{center}
    \tabulinesep=1.2mm
\begin{tabu} to \linewidth { |[1.5pt] c | *{2}{X[1 c]|}[1.5pt] }
    \tabucline[1.5pt]{-}
\rowfont{\bfseries}
Parameter   &   Value       &   Units       \\ 
    \tabucline[1.5pt]{-}
\multicolumn{3}{ |[1.5pt]c|[1.5pt] }{Nose Parameters} \\ \tabucline[1.5pt]{-}
$\alpha$    & 10            & Deg           \\ 
    \tabucline[1.5pt]{-}
$[V_{x}(0), V_{y}(0), V_{z}(0)]_{\text{Wind Error}}$ 
            & [0, -6, 0]    & m/s           \\ 
    \tabucline[1.5pt]{-}
\end{tabu}
    \end{center}
\end{document}

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