Question 1092858
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{{{sin^4(2theta)-2sin^2(2theta)}}} = -1  ====>

{{{sin^4(2theta)-2sin^2(2theta) + 1}}} = 0  ====>

{{{(sin^2(2theta) - 1)^2}}} = 0  ====>

{{{sin^2(2theta) - 1}}} = 0  ====>

{{{(sin(2theta) - 1)*(sin(2theta)+1)}}} = 0  ====>


There are two ways to continue:


1)   {{{sin(2theta)}}} = 1  ====>  {{{theta}}} = {{{pi/4}}}  and/or  {{{theta}}} = {{{5pi/4}}}.


2)   {{{sin(2theta)}}} = -1  ====>  {{{theta}}} = {{{3pi/4}}}  and/or  {{{theta}}} = {{{7pi/4}}}.


<U>Answer</U>.  The original equation has 4 roots in the interval [0,{{{2pi}}}):


         {{{theta}}} = {{{pi/4}}},  {{{3pi/4}}},  {{{5pi/4}}}  and  {{{7pi/4}}}.
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