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Question

Solve:
sin2π3+sin22π3+sin25π3+sin28π3=3

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Solution

sin2π3+sin22π3+sin25π3+sin28π3
=(32)2+(32)2+sin2(2ππ3)+sin2(3ππ3)
=34+34+(sinπ3)2+(sin(π3))2
=34+34+34+34
124
=3.


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