Spin-stabilization offers a straightforward but robust attitude control. For Earth-orbiting satellites, attitude determination can be done by Sun and Earth sensor measurements. For deep space missions, however, valid Earth sensor measurements are not available. The paper presents a technique for the determination of the spin axis orientation using only Sun sensor data, collected at two different instants of time. The spin axis attitude follows from the intersection of the two Sun angle cones. The application of the TSC method was validated using actual in-orbit Sun sensor measurements of CONTOUR. The results show that an attitude accuracy of 1 deg can be reached after an interval of only a few hours and 0.1 deg can be achieved after a 2-days interval.