I think you have been quite lucky there but i dont think its a golden eagle. Being that you are in the outer hebs and not very far from the sea i think you have captured what we used to call a flying door. I think it is most likely a Sea Eagle or its proper name a white tailed or grey sea eagle.
They are becoming the norm around the bays and inlets of Lewis and Harris and i trudged the isles looking for them a few years ago with little success until i was about to get on the ferry and right in front of us were about 4 of them all playing, soaring and feeding in the bay.
The difference can (when close up) be easy to spot (white tail obviously and a very golden brown head on the golden) but from a distance it can be very difficult. The sea eagles tend to be close to the coast or water and appear very black the goldens appear more rusty brown and have occasional greyer or whitish brown feathering below the wings - giving it a lighter look to the sea eagle, the sea eagle is a bit larger than the golden and has a distinctive flat 'door like' wing when soaring. Goldens are more heathland and mountains and forest (i had the beejeebies scared out of me in the lake district once when a golden swooped out of a set of pines along the track i was walking - under the tree canopy and nearly took my head off..).
The Sea eagle populations on Harris and Lewis are from what i remember doing extremely well and i think their numbers are still on the increase, as such if you see one then you will probably see two or three all close together, the goldens however are far more recluse and you will be very lucky to see one.
Looking closely at your photo i think its a Sea Eagle. Another birdy might be able to correct me if i am wrong, either way, great spot.
Canon 550D, Canon EFS 17-85 IS USM, Canon EF 75-300 IS USM, Canon EFS 10-22mm USM, Canon EF35mm F2.
Got some of the gear but really still no idea...