Question 1000791
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Hello,


introduce the new variable  y = sin(x).  You will get a quadratic equation for  y


{{{2y^2 + 3y + 1}}} = {{{0}}}.


Solve it and find  y:   y = {{{-1/2}}}  and  y = -1.


Then determine x:


Case 1:   y = {{{-1/2}}}   --->   sin(x) = {{{-1/2}}}   --->   x = 210° + k*360°  and  x = 330° + k*360°.


Case 2:   y = {{{-1}}}   --->   sin(x) = {{{-1}}}   --->   x = 270° + k*360°


It is the standard way of solving non-linear equations.