If a , b , c ∈ ( 0 , π ) and a + b + c = π ,
Then, Find the value of
sin ( b ) . sin ( c ) . sin ( b − c ) ( sin 2 ( b ) + sin 2 ( c ) + sin 2 ( b − c ) ) + sin ( c ) . sin ( a ) sin ( c − a ) ( sin 2 ( c ) + sin 2 ( a ) + sin 2 ( c − a ) ) + sin ( a ) . sin ( b ) . sin ( a − b ) ( sin 2 ( a ) + sin 2 ( b ) + sin 2 ( a − b ) ) + sin ( b − c ) sin ( c − a ) sin ( a − b ) ( sin 2 ( b − c ) + sin 2 ( c − a ) + sin 2 ( a − b ) )
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Yeah.... guessing.... this problem is a worth 10 seconds one right ?
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This problem inspired my new note that I'll be posting shortly: guessing.