Question 366464
{{{sin (theta) + csc (theta) = 5/2}}},
{{{sin (theta) +1/sin (theta) = 5/2}}},
{{{((sin (theta))^2 +1)/sin(theta) = 5/2}}},
{{{2(sin (theta))^2 +2= 5sin(theta) }}},
{{{2(sin (theta))^2 - 5sin(theta)+2= 0}}},
{{{(2sin(theta)-1)(sin(theta)-2) = 0}}}.  The first factor gives 
{{{2sin(theta) = 1}}}, or {{{sin(theta)=1/2}}}, giving {{{theta}}} = 30 or 150 degrees.
The second factor {{{sin(theta)-2 = 0}}} does not give any solutions. (Why?)