AymanHossam - July 28, 2013 at 11:32pm
Yes, you can directly upgrade from your current 6.1.3 directly to iOS7 beta 3.
You just download the .dmg file and extract it using any dmg extractor if you are on a windows platform, or using XCode if you are on an apple computer.
Get the ipsw file, connect your iphone/ipad to iTunes, and through iTunes, press shift while clicking the Check for Update button. Pick the ipsw file and start the upgrade process which took around 7-10 minutes on my iPhone 5.
An important note, check your device model number and download the corresponding version of the beta 3 software.
Hope this helped