Question 1147254
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First divide both sides by 9. You will get an EQUIVALENT equation


    cos(2theta) = - cos(theta)


Next, use the <U>standard basic trigonometry formula</U>


    cos(2theta) = 2*cos^2(theta) - 1.


Then equation (1) takes the form


    cos^2(theta) = -cos(theta),   or


    cos^2(theta) + cos(theta) = 0.


Factor it


    cos(theta)*(cos(theta) + 1) = 0.


Hence, EITHER  cos(theta) = 0,  giving solutions  {{{theta}}} = {{{+- pi/2}}} + {{{2k*pi}}},  k = 0, +-1, +-2, . . . 


       OR  cos(theta) = -1,  giving solutions  {{{theta}}} = {{{(2k+1)*pi}}},  k = 0, +-1, +-2, . . . 
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Completed, solved and explained in all details, with steps.