Find real q such that `(3+2isintheta)/(1-2isintheta)` is purely real.

Explanation

`z = (3+ 2 i sin theta)/(1-2i sin theta) = (3+ 2i sin theta)/(1-2 sin theta) .(1+ 2i sin theta)/(1+ 2isin theta)`
`z = ((3+ 2 i sin theta)( 1 + 2isin theta))/(1 + 4 sin^(2) theta)`
`= (3-4 sin^(2) theta + 8i sin theta)/( 1 + 4 sin ^(2) theta)`
Now z is purely real if ` sin theta = 0 or theta = npi, n in Z`
Also , z is purely imaginary if
`3-4 sin^(2) theta = 0`
or `sin theta = 0`
`rArr theta = npipm (pi)/(3), n in Z`