Question 1098979
Use a substitution,
{{{u=sin(2*theta)}}}
Then,
{{{u^2-5u-1=0}}}
Complete the square,
{{{u^2-5u+(5/2)^2-1=(5/2)^2}}}
{{{(u+5/2)^2=25/4+4/4}}}
{{{(u+5/2)^2=29/4}}}
{{{u+5/2=0 +- sqrt(29)/2}}}
{{{u=-5/2 +- sqrt(29)/2}}}
Only one solution is valid since {{{-5/2-sqrt(29/2)<-1}}}.
{{{sin(2*theta)=-5/2+sqrt(29)/2}}}
{{{sin(2*theta)=-0.19258}}}
Two solutions,
{{{theta=95.6}}} and 
{{{theta=174.5}}}