The total number of real solutions of the equation \( \theta = \tan^{-1}(2 \tan \theta) - \dfrac{1}{2}\sin^{-1}\!\left(\dfrac{6 \tan \theta}{9 + \tan^{2}\theta}\right) \) is
(Here, the inverse trigonometric functions \( \sin^{-1} x \) and \( \tan^{-1} x \) assume values in \( \left[-\dfrac{\pi}{2}, \dfrac{\pi}{2}\right] \) and \( \left(-\dfrac{\pi}{2}, \dfrac{\pi}{2}\right) \), respectively.)
