Question 2
Prove that there exist 1977 triangles whose angles $A,B,C$ satisfy
$$\frac{\sin A+\sin B+\sin C}{\cos A+\cos B+\cos C}=\frac{12}{7},\qquad \sin A\sin B\sin C=\frac{12}{25}.$$
$$\frac{\sin A+\sin B+\sin C}{\cos A+\cos B+\cos C}=\frac{12}{7},\qquad \sin A\sin B\sin C=\frac{12}{25}.$$