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Since maximum value of sinβ is 1, (where β is any angle)

the value of sin a, sin b and sin c must be equal to 1 . for any other values, the condition that sin a+sin b+sin c=3 would not satisfy.

so sin a = sin b = sin c = 1

sin² a + sin² b + sin² c = 1² + 1² + 1² = 3

the value of sin a, sin b and sin c must be equal to 1 . for any other values, the condition that sin a+sin b+sin c=3 would not satisfy.

so sin a = sin b = sin c = 1

sin² a + sin² b + sin² c = 1² + 1² + 1² = 3

by hit and trial method we can say that

sina=sinb=sinc=sin90

sin2a=2sinacosa

sin2b=2sinbcosb

sin2c=2sinccosc

sina=1 ,cosa=0

sinb=1 ,cosb=0

sinc=1 ,cosc=0

sin2a+sin2b+sin2c=0