How to install iOS 7 Beta without UDID / Developers account:
Step 1: Launch iTunes and connect your iPhone with your PC via USB cable.
Step 2: Right click on your iDevice on iTunes and take a backup (or backup to iCloue)
Step 3: Restore your iPhone to iOS 6.1.3 (or 6.1.4 if you have iPhone 5)
Step 4: Set up as new iPhone – do not restore from backup.
Step 5: Hold down the Option key in OS X (Windows use Shift key) and click on “Update” not on “Restore”
Step 6: Select the iOS 7 beta file you downloaded, updating the device to iOS 7 beta. Done