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Easy

Question

The sum of all the solution of $cot invisible function application theta equals sin invisible function application 2 theta comma blank open parentheses theta not equal to n pi comma n blank i n t e g e r close parentheses comma blank 0 less or equal than theta less or equal than pi blank$ is

$3 π / 2$
$π$
$3 π / 4$
$2 π$

The correct answer is: $3 pi divided by 2$

From the given relation
$cos invisible function application theta equals open parentheses 2 sin invisible function application theta cos invisible function application theta close parentheses sin invisible function application theta comma sin invisible function application theta not equal to 0$
$rightwards double arrow sin invisible function application theta equals plus-or-minus fraction numerator 1 over denominator square root of 2 end fraction blank o r cos invisible function application theta equals 0$
$rightwards double arrow theta equals fraction numerator pi over denominator 4 end fraction comma fraction numerator 3 pi over denominator 4 end fraction comma fraction numerator pi over denominator 2 end fraction open parentheses because theta element of open square brackets 0 comma blank pi close square brackets close parentheses$
Then the sum of roots is $fraction numerator 3 pi over denominator 2 end fraction$

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