First Officer reported after the gear handle was selected to the down position; both the main landing gear indicated a triple chime and a 'GEAR DISAGREE' aural a few seconds after selecting gear down. This was followed by an amber HYD 3 LO PRESS message and the hydraulic synoptic page displayed 0% in the HYD 3 reservoir. The flight crew performed a go around to a landing.

Narrative

Aircraft X. ZZZ1-ZZZ. Upon interception of the [Runway] XXL glide slope into ZZZ; the Captain called for gear down. The gear was selected down and in a normal amount of time; the nose gear was down and locked showing a green indication. As for both the main landing gear; we were given a triple chime and a 'GEAR DISAGREE' aural a few seconds after selecting gear down. The approach was discontinued and we were given a 180 degree heading from ATC to turn away from the airport. When flying this 180 degree heading and probably about 30 seconds after receiving the GEAR DISAGREE Master Warning; an amber HYD 3 LO PRESS was displayed on the EICAS. The hydraulic synoptic page displayed 0% in the HYD 3 reservoir. The GEAR DISAGREE QRH was ran first; and it resulted in a manual extension of the gear. When the gear handle was pulled; both mains showed a green indication about 5 second after. The HYD 3 LO PRESS QRH was ran next. Upon completion of both checklists; we had flown about 1 complete box pattern outside the airport. The Captain decided to [request priority handling] at that time and communicated that we'd need equipment standing by. ATC asked if we could land on [Runway] XY and we accepted. An additional box pattern was flown to give us time to brief Dispatch; the Flight Attendant; and the passengers. This also gave us time to set up the new approach. The Captain had elected to have the Flight Attendant prepare for [the situation]. No evacuation was required. The aircraft came to a stop on the runway around roughly XA:40. We had roughly 1;800 pounds of gas on board. There was a noticeable shimmy with the nose gear as we slowed down. We stayed on the runway due to the loss of nose wheel steering. Operations circled the plane to see if there were any leaks. None were observed. The Captain and I communicated with Maintenance Control and Operations for a tug. After about 15 minutes; we were tugged in and parked at the gate.The ultimate cause of the issues was the lack of hydraulic fluid in system 3. This caused the HYD 3 LO PRESS caution; as well as the GEAR DISAGREE when selecting gear down.