Square-Trigonometry Equations!

Geometry Level 2

\[\dfrac1{\sin^2{\theta}}-\dfrac1{\cos^2{\theta}}-\dfrac1{\tan^2{\theta}}-\dfrac1{\cot^2{\theta}}-\dfrac1{\sec^2{\theta}}-\dfrac1{\csc^2{\theta}}=-3\]

Find the number of solutions of \(\theta\) in the interval \((0,2\pi)\) that satisfy the equation above.

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