Question 969313
<pre>
{{{3sin^2(theta)-5sin(theta)+2}}}}{{{""=""}}}{{{"0"}}}

{{{matrix(1,2, Use, u-substitution)}}}

{{{matrix(1,4,Let,sin(theta),""="",u)}}}

{{{matrix(1,4,Then,sin^2(theta),""="",u^2)}}}

{{{3u^2-5u+2}}}{{{""=""}}}{{{"0"}}}

{{{(3u-1)(u-2)}}}{{{""=""}}}{{{"0"}}}

{{{3u-1=0}}},  {{{u-2=0}}}
{{{3u=1}}},      {{{u=2}}}
{{{u=1/3}}}

{{{matrix(1,5,  Now, substitute, sin(theta), for, u)}}}
 
{{{sin(theta)=1/3}}},   {{{cross(sin(theta)=2)}}}

We discard the second answer since the sine can only be
between -1 and +1.

Use the inverse sine function to get the value for <font face="symbol">q</font>.

I'll let you finish, since you did not specify whether you want
degrees or radians, or whether you only want answers between 0° 
and 360°, or between 0 an 2<font face="symbol">p</font> or whether you wanted a general 
solution in terms of an arbitrary integer n.

Edwin</pre>