The Google Chromecast (2015) works great with other Android based products like the Sony Xperia Z3+, Z4, and Z5 and the Sony Bravia 4K Ultra HD Smart LED TV.
First connect Google Chromecast to one of the Sony 4K TV's HDMI ports. You can plug a USB cable from the Sony TV to the Chromecast in order to provide power. There is no power button on the Chromecast that needs to be pressed.
On the Sony 4K TV, after selecting the HDMI input that the Chromecast is plugged into you should see the Chromecast setup screen.
Install the Chromecast application from Google Play on the Xperia. Once installed, go ahead and open the Chromecast App and select Devices tab at the top.
Choose the Chromecast you are installing and select Set Up.
Once you see the code on bottom right of the TV matches that shown on the App, select "I See The Code". You can then change your Chromecast name or just leave it as it is and select Set Name.
Once the setup is done, you can then choose the WI-FI network for your Chromecast to connect to.
The Chromecast App also acts as a gateway to different content and apps on your Xperia that take advantage of Chromecast like Chrome and YouTube. You can select the Get Apps tab to find more Apps that make use of Chromecast. YouTube is the most popular application given the ability to cast any video from your Xperia to your TV.