Geometry

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Let ƒÆ=sin −1 7 25 . Consider the sequence of values defined by a n =sin(nƒÆ) . They satisfy the recurrence relation
a n+2 =k 1 a n+1 +k 0 a n ,n¸N
for some (fixed) real numbers k 1 ,k 0 . The sum k 1 +k 0 can be written as p q , where p and q are positive coprime integers. What is the value of p+q ?

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