Shell script with getopt for short and long options -handling option with and without argument

Wanted to run a script -- with option ./myscript.sh -a -g test -- without option ./myscript.sh -a -g The script looks like in below snippet, but don't see below script working correctly. The getopt for options specified with :: (like g:: or gamma::) upon parsing g or gamma the passed argument is moved to end every time includes empty argument user option: --gamma '' -a -- 'test'. Refer the output of the script

$ sh optionwithandwithoutarg.sh --gamma test -a
user option:  --gamma '' -a -- 'test'
arg info :- --gamma
arg info :- -a
arg info :- --
Alpha flag: true
Beta value: ''
Gamma value: 'default_gamma'
Remaining arguments: 'test'

## Script code used

#!/bin/bash

OPTIONS=$(getopt -o a,g::,b: --long alpha,gamma::,beta: --name "$0" -- "$@")

if [ $? -ne 0 ]; then
    echo "Error: Invalid options provided."
    exit 1
fi

echo "user option: $OPTIONS"

eval set -- "$OPTIONS"

# Initialize variables
ALPHA_FLAG="false"
BETA_VALUE=""
GAMMA_VALUE=""

while true; do
    echo "arg info :- $1"
    case "$1" in
        -a | --alpha)
            ALPHA_FLAG="true"
            shift
            ;;
        -b | --beta)
            BETA_VALUE="$2"
            shift 2
            ;;
        -g | --gamma)
            if [[ "$2" != "--" && -n "$2" ]]; then
                GAMMA_VALUE="$2"
                shift 2
            else
                GAMMA_VALUE="default_gamma" # Assign a default if no argument given
                shift 2
            fi
            ;;
        --)
            shift
            break
            ;;
        *)
            echo "Not supported option"
            exit 1
            ;;
    esac
done

echo "Alpha flag: $ALPHA_FLAG"
echo "Beta value: '$BETA_VALUE'"
echo "Gamma value: '$GAMMA_VALUE'"
echo "Remaining arguments: '$*'"

How to handle the options with and without argument with getopt