6.2. In an isosceles triangle \(ABC\), one of the angles is equal to the difference of the other two, and one of the angles is twice another. The angle bisectors of angles \(A\), \(B\), and \(C\) intersect the circumcircle of the triangle at points \(L\), \(O\), and \(M\) respectively. Find the area of triangle \(LOM\), if the area of triangle \(ABC\) is 2. If the answer is not an integer, round it to the nearest integer.
Answer: 3. Instructions. Exact answer: $\sqrt{3}+1$.