Michael keeps it real

Algebra Level 4

For a uniformly random real number kk in the interval [10,0],[-10, 0], the probability that sin4θsin2θk=0\sin^4 \theta - \sin^2 \theta - k = 0 has at least one real solution θ\theta can be expressed as ab\dfrac{a}{b} for positive coprime integers aa and b.b. What is the value of a+ba+b?

This problem is posed by Michael T.

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