SOLUTION: The exact value of {{{cos(pi/7)+cos^2(pi/7)-2cos^3(pi/7)}}} is a rational number in the form p/q, where p and q are integers. Find (p+q)

, solving for cos2(x),







So we solve this for  cos3(x),



Solving for cos3(x)



So 






 
(expression 1):   

Expression 1 is what we must evaluate.  

  










(equation 2)  



We set the real part of the left side of equation 2 
equal to the real part of the right side of equation 2.

 

Now we use identities of angles subtracted from pi to reduce
the angles:





Substituting

  

 



(equation 3):   

Now we go back to expression (1)

(expression 1):   

and use equation 3 to substitute 1/2 for the first three terms in 
the parentheses of expression (1):



So 

and 

Edwin