VN-TST 1985 Problem 3

Does there exist a triangle $ABC$ satisfying the following two conditions: (a) ${ \sin^2A + \sin^2B + \sin^2C = \cot A + \cot B + \cot C}$ (b) $S\ge a^2 - (b - c)^2$ where $S$ is the area of the triangle $ABC$ .