Let sin^2x=a, cos^2x=b
a+b=1
a^4+b^4=17/32
Let S(n)=a^n+b^n
S(0)=2
S(1)=1
Characteristic equation:
(x-a)(x-b)=0
x^2=(a+b)x-ab
S(n+2)=S(n+1)-abS(n)
S(2)=S(1)-abS(n)=1-2ab
S(3)=S(2)-abS(1)=1-2ab-ab=1-3ab
S(4)=S(3)-abS(2)=1-3ab-ab(1-2ab)=2(ab)^2-4ab+1=17/32
64(ab)^2-128ab+15=0
(8ab-15)(8ab-1)=0
ab=15/8(rejected) or ab=1/8

ab=1/8
sinxcosx=(+/-)1/2sqrt2
sin2x=(+/-)1/sqrt2
2x=(n/2)pi+pi/4
x=(n/4)pi+pi/8 for some integer n

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