If you can wire PLAY:3 to your network, BRIDGE has no purpose. At this age BRIDGE is considered obsolete and many issues have been reported. The best plan is to retire BRIDGE. BRIDGE was developed before SONOS could be connected to WiFi and consumer WiFi was not as developed as it is now. Back then it was required that at least one SONOS unit was wired to the network. BRIDGE could satisfy that requirement if it was inconvenient to wire a player. Now, SONOS supports WiFi.

I still prefer wired connections (without BRIDGE). If you want PLAY:3 to be wireless, power down BRIDGE, temporarily wire PLAY:3 to the network, then update network settings. If there is already a player using WiFi, the PLAY:3’s network settings might already be updated, but don’t assume this. PLAY:3 can be quirky about this, you still may need to reboot and, at least temporarily, wire it to the network.

Note that all Sonos devices require some sort of ‘network’ connection, they can’t be ‘directly connected’ to a Mac/PC, but need instead to be connected with your router. It’s slightly different if you’re using the line in, but since you mentioned ‘through Ethernet’…

Edit…and there is no line in on a PLAY:3 anyway…

With the PLAY:3 connected to the network, wired or wireless, you can use a SONOS controller running on a computer/phone/pad to play music services or music stored on the computer or local storage device on the PLAY:3. You cannot send raw audio output from the computer directly to the PLAY:3