Square-Trigonometry Equations!

Geometry Level 2

1sin2θ1cos2θ1tan2θ1cot2θ1sec2θ1csc2θ=3\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 θ\theta in the interval (0,2π)(0,2\pi) that satisfy the equation above.

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