WiMax is a radio communications standard, so locating the origin of a broadcast signal is of course possible whenever you're transmitting.
As implemented in cellular networks, such as LTE, the coverage will overlap and the protocol will provide means of switching between masts as you move between cells. This means you will likely be within contact from two or three masts at any one time, hence triangulating your location is completely possible whenever your device is on the network, just as it is with current GSM cell networks.
As far as co-operation from your device, of course if you can control when your device transmits, you can make it difficult to determine your location by only communicating with a single mast at a time, meaning you can only be determined to lie somewhere on a circumference at a radial point that is the determined distance you are from that mast, bearing in mind however that you will usually also be identified as being on a certain arc at that distance which is usually 120 degrees or so. This is known as the azimuth of the mast you're connected to.
As soon as you communicate with two or more masts, your position becomes very precise. The patent you referred to covers determining your location from two base stations meaning your location is an estimate of being somewhere in the regions where the two range rings overlap. In practice, a few things are different from the image below. First as an azimuth is known, depending on the length of its arc it might be enough to rule out one of possible intersects (that would exist if it were a single radial antenna), meaning you location is anywhere where the lines are intersecting (a physical area in practice). Secondly the lines shown below would typically be thicker indicating that the area you are within is only known to a given precision, which I recall is still usually enough to implicate you as being in a certain building (say, an area of 20 metres that looks roughly like a square on a map).