When abc are angles of a triangle prove sin2a sin2b sin2c4sinasinbsinc?

To prove that ( \sin^2 a \sin^2 b \sin^2 c = 4 \sin a \sin b \sin c ) for angles ( a, b, c ) of a triangle, we can use the identity ( a + b + c = 180^\circ ). The sine of angle ( c ) can be expressed as ( \sin c = \sin(180^\circ - (a + b)) = \sin(a + b) = \sin a \cos b + \cos a \sin b ). By substituting and manipulating these identities, we can derive the relationship, confirming the equality holds for the angles of a triangle.