How do I install VLC 3.0 on Ubuntu Zesty 17.04?

You can install a snap of vlc 3:

sudo snap install vlc

It will be installed alongside your original vlc (if you don't uninstall the original vlc).

I prefer flatpak over snap. It's open source and multi arch application sandboxing and distribution framework for Linux. It's easy to use and you can run closed source applications such as Steam, Sublimetext in it.

You can install it via ppa or build it straight from github, it doesn't take much time. What I did for my Ubuntu 16.04

mkdir FLATPAK; cd FLATPAK

git clone --recurse-submodules https://github.com/ostreedev/ostree.git
cd ostree
git submodule update --init
env NOCONFIGURE=1 ./autogen.sh
./configure
make
sudo make install
cd ..
git clone https://github.com/flatpak/flatpak.git
cd flatpak
./autogen.sh
make
sudo make install
cd ..
git clone https://github.com/PipeWire/pipewire.git
cd pipewire
./autogen.sh
make
sudo make install
cd ..
git clone https://github.com/flatpak/xdg-desktop-portal.git
./autogen.sh
make
sudo make install
cd ..
git clone https://github.com/flatpak/xdg-desktop-portal-gtk.git
./autogen.sh
./configure
make 
sudo make install

then add application repositories to install applications.

flatpak --user remote-add --if-not-exists flathub https://flathub.org/repo/flathub.flatpakrepo

Finally install VLC

flatpak --user install flathub org.videolan.VLC

and launch it via

flatpak run org.videolan.VLC

To see available applications and runtimes

 flatpak --user remote-ls -d flathub

For more info check out Flatpak

EDIT: I added new dependencies and changed order of installation sequence.