HINT Eventually you will need to factor Just before factorin

HINT: Eventually you will need to factor. Just before factoring, try multiplying both sides of the equation by 2 to get rid of the fraction.

Solution

cot^2 theta=(3/2)csc theta

cot theta=cos theta/sin theta

and csc theta=1/sin theta

cos^2 theta/sin^2 theta= (3/2sin theta)

2 cos ^2 theta= 3sin theta

and cos^2 theta= 1- sin^2 theta

2(1-sin^2 theta)= 3 sin theta

2-2sin^2 theta= 3sin theta

2sin^2 theta -3sin theta -2=0

(sin theta -2)(2sin theta +1)=0

sin theta=2 and sin theta=-1/2

we have to ignore sin theta=2 since sin theta lies between -1 and 1

therefore sin theta=-1/2

theta= 7pi/ 6 , 11pi/6