Question:

<p><strong>Step 1:</strong> Expand the left side: \((\sin A + \sin B)^2 - \sin^2 C = 3\sin A\sin B\)</p><p><strong>Step 2:</strong> Expand and rearrange: \(\sin^2 A - \sin^2 C + \sin^2 B = \sin A\sin B\)</p><p><strong>Step 3:</strong> Use \(\sin(A+C)\sin(A-C) + \sin^2 B = \sin A\sin B\)</p><p><strong>Step 4:</strong> Since \(A + C = \pi - B\), we have \(\sin(A+C) = \sin B\)</p><p>\(\sin B[\sin(A-C) + \sin(A+C)] = \sin A\sin B\)</p><p><strong>Step 5:</strong> Simplify (assuming \(\sin B \neq 0\)): \(2\sin A\cos C = \sin A\)</p><p>\(\cos C = \frac{1}{2}\) ⟹ \(C = 60°\)</p><p>∴ \(\frac{C}{10} = 6°\)</p>