Solve the equation for the interval $[0,2pi).$

$2sine$ squared left parenthesis $x$ right parenthesisequalssine left parenthesis $x$ right parenthesis

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Part $1$

$A.$StartSet StartFraction $pi$ Over $2$ EndFraction comma StartFraction $3pi$ Over $2$ EndFraction comma StartFraction $pi$ Over $3$ EndFraction comma StartFraction $2pi$ Over $3$ EndFraction EndSet $nbsp$

StartSet StartFraction $pi$ Over $2$ EndFraction comma StartFraction $3pi$ Over $2$ EndFraction comma StartFraction $pi$ Over $3$ EndFraction comma StartFraction $2pi$ Over $3$ EndFraction EndSet $nbsp$

$B.$StartSet StartFraction $pi$ Over $3$ EndFraction comma StartFraction $2pi$ Over $3$ EndFraction EndSet $nbsp$

StartSet StartFraction $pi$ Over $3$ EndFraction comma StartFraction $2pi$ Over $3$ EndFraction EndSet $nbsp$

$C.$StartSet StartFraction $pi$ Over $6$ EndFraction comma StartFraction $5pi$ Over $6$ EndFraction EndSet $nbsp$

StartSet StartFraction $pi$ Over $6$ EndFraction comma StartFraction $5pi$ Over $6$ EndFraction EndSet $nbsp$

$D.$StartSet $0$ comma $pi$ comma StartFraction $pi$ Over $6$ EndFraction comma StartFraction $5pi$ Over $6$ EndFraction EndSet $nbsp$

StartSet $0$ comma $pi$ comma StartFraction $pi$ Over $6$ EndFraction comma StartFraction $5pi$ Over $6$ EndFraction EndSet $nbsp$