Question 1082015
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<U>Case 1.</U>


<pre>
{{{tan(4*theta)}}} = 0  ====>

{{{4*theta}}} = 0  or  {{pi}}}  or  {{{2pi}}}  or  {{{3pi}}}  ====>

{{{theta}}} = 0,  {{{pi/4}}},  {{{pi}}},  and  {{{3pi/4}}}.


<U>Answer</U>. There are 4 solutions in the interval [{{{0}}},{{{2pi}}}):

        {{{theta}}} = 0,  {{{pi/4}}},  {{{pi}}},  and  {{{3pi/4}}}.
</pre>

<U>Case 2</U>


<pre>
{{{tan(4*theta)}}} = 1.   ====> 

{{{4*theta}}} = {{{pi/4}}}  or  {{{pi/4 + pi}}}  or  {{{pi/4 + 2pi}}}  or  {{{pi/4 + 3pi}}}  ====>

{{{theta}}} = {{{pi/16}}}  or  {{{pi/16 + pi/4}}}  or  {{{pi/16 + pi/2}}}  or {{{pi/16 + 3pi/2}}}.


<U>Answer</U>.   There are 4 solutions in the interval [{{{0}}},{{{2pi}}}):

          {{{theta}}} = {{{pi/16}}},  {{{5pi/16}}},  {{{19pi/16}}},  {{{25pi/16}}}.
</pre>