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Dear Arnab,
cos[alpha]+cos[beta]+cos[gamma]=3 -------1
this can only be possible when cos[alpha] ,cos [beta] ,cos [gamma] are all equal to 1
for no other value of cos[alpha] ,cos [beta] ,cos [gamma] the equation 1 holds true as max value of cosine is 1.
the values of alpha , beta , gamma are all 2npie where n is any integer and for this value
so sin[alpha] = sin[beta] = sin [gamma] =0
so their sum is also 0
so answer is 0
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