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int(0)^( pi/2)(2log sin x-log sin2x)dx...

int_(0)^( pi/2)(2log sin x-log sin2x)dx

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By using the properties of definite integrals, evaluate the integrals int_(0)^(pi/2)(2log sin x log sin 2x)dx

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int_(0)^((pi)/(2))(2log cos x-log sin2x)dx