Question 1068830
{{{theta=0^o}}} and {{{theta=180^o}}} are solutions because they make {{{tan(theta)=0}}}
There are four more solutions that make
{{{sin(theta)=sqrt(11)/5}}} or {{{sin(theta)=-sqrt(11)/5}}} .
My calculator says that {{{sin(theta)=sqrt(11)/5}}}
corresponds to {{{highlight(theta=41.55^o)}}} .
That means that {{{theta=180^o-41.55^o=highlight(138.45^o)}}} also has {{{sin(theta)=sqrt(11)/5}}} .
The calculator would also say that {{{theta=-41.55^o}}} has {{{sin(theta)=-sqrt(11)/5}}} .
That is not a solution, because it is negative,
but we know that {{{-41.55^o}}} is co-terminal with
{{{theta = 360^o-41.55^o=358.45^o}}} , which is a solution.
And since we know that {{{sin(360^o-theta)=-sin(theta)}}} ,
from the solutions that make {{{sin(theta)=sqrt(11)/5}}} ,
we can get the solutions that make {{{sin(theta)=-sqrt(11)/5}}} :
{{{theta=360^o-41.55^o=highlight(358.45^o)}}}  and
{{{theta=360^o-138.45^o=highlight(221.55^o)}}}