IMPORTANT: If you're using an ipad or iphone to join the room via a web browser and you're having trouble connecting, use Safari, not Chrome or another web browser. Apple may limit the capabilities of browsers other than their own Safari, preventing non-Safari browsers from being used for the required web communication protocols. Using the apps avoids this issue.
Click on the Mobile App Info button (the phone-like icon circled in red in the image above) to bring up a window that includes a link to the app, along with your credentials that authorize you to connect to the BCT room. The window appears as shown here, though the email and pin are blurred out in the image. You can also bring up this window by expanding the options menu (the three horizontal lines) and selecting the Mobile App Info button that appears.
Choose the app store button that applies to your device (Android or Apple - clicking on the icons will take you to the app in the appropriate store) and download and install the app to your device.
Open the app and enter the email and pin credentials provided at the bottom of the Mobile App Info dialog box. Follow the instructions in the app, and use the Sync All Available Rooms button in the app if both rooms aren't available to you.
It does not appear that you can join both rooms simultaneously from the same device, but you could use another device (e.g. a tablet or phone) or the web-based version to be in both.