I am connected to a WPA/WPA2 Access Point and I want to sniff all wireless traffic inside that network. How can I decrypt the traffic even though I don't have the pre-shared key?
No, you need the pre-shared key.
WPA-PSK and WPA2-PSK encrypt traffic per client and session keys, which are derived from the pre-shared key.
So if you know the pre-shared key for the network (which you don't) and you sniff the four way handshake when another client joins the access point, you could decrypt only that client's traffic.
This only applies assuming access point isolation is not enabled on the access point.