WORK OUT THIS
sin(A+B+C)

Your question has been heard loud and clear.

sin (A + B + C) = sin [( A + B) + C]

                    = sin (A + B) cos C + cos (A + B) sin C, [applying the formula of sin (α + β)]

                     = (sin A cos B + cos A sin B) cos C + (cos A cos B - sin A sin B) sin C, [applying the formula of sin (α + β) and cos (α + β)]

                      = sin A cos B cos C + sin B cos C cos A + sin C cos A cos B - sin A sin B sin C, [applying distributive property]                

                      = cos A cos B cos C (tan A + tan B + tan C - tan A tan B tan C)

therefore the expansion of sin (A + B + C) = cos A cos B cos C (tan A + tan B + tan C - tan A tan B tan C).