# Michael keeps it real

Algebra Level 4

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

This problem is posed by Michael T.

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