Golang waitgroup doesn't synchronize

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Go

Golang

This abstract code will display "true" in a loop as long as channel receives new messages.

package main

import (
	"fmt"
	"sync"
)

var a = make(chan bool)
var wg sync.WaitGroup

func main() {
	wg.Add(1)
	go test()
	for i := 0; i < 2; i++ {
		wg.Add(1)
		go test2()
	}
	wg.Wait()
}

func test() {
	for val := range a {
		fmt.Println(val)
	}
	wg.Done()
}

func test2() {
	for i := 0; i < 3; i++ {
		a <- true
	}
	wg.Done()
}

What I have tried:

The problem is that WaitGroups do not synchronize it as advertised. Despite channel being unused at the end wg.Done() is never called, and application ends with a deadlock. I also can't close the channel, because multiple test2 functions access the same channel.