Towering over downtown Sarajevo, Trebević is an extremely popular mountain for hiking and trail running nearly year round. Trebević was the setting for multiple events during the 1984 Winter Olympics in Sarajevo and most routes up the mountain travel past the old, graffitied, bullet pocked Olympic luge track. This route starts at the Latin Bridge, site of Archduke Ferdinand's assassination and in the heart of downtown Sarajevo, and finishes at the summit monument. Note this effort does not terminate at the radio towers, you need to tag the summit monument.
The attached GPX route is one of the most direct routes up the mountain. The initial route through the city could be changed slightly to the west to be a little faster. Variations are allowed, but the start is fixed at the south side of the Latin Bridge over the river Miljacka (First attached photo) and the finish is at the summit monument/pillar on top (Last attached photo). Following the GPX track, the first couple of miles will be steep climbing on concrete streets. At the end of the road, the route will continue steeply up a rutted single track path to the ridgeline. At the ridge, the route will climb steeply on asphalt until you pass under the luge track, from here it will continue a little more than a kilometer flat on asphalt before reaching a large parking area with a hotel. You are roughly halfway (550 meters) to the summit. Follow the road to the right past the hotel and then begin climbing steeply on a dirt trail. From here, there are alot of options to the summit. The attached GPX goes up a downhill MTB course. Other than about 50 meters of flat, the trail is almost a direct climb to the summit. 100 vertical meters below the summit the MTB trail connects to a dirt fire road. Follow the fire road to the final summit trail, gain the ridge, and traverse to the summit monument. Tag the summit pillar and return downtown, stop your time at the bridge.