If cotangent theta is equal to 2 thirds , what is the value of cosecant theta ?

Since cotangent is adjacent over opposite, the sides can be taken as 2 and 3. The hypotenuse is √(2² + 3²) = √13, so cosecant, hypotenuse over opposite, is √13/3. Thus the correct choice is the fraction with numerator √13 and denominator 3.

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