| (A) | 1 | (B) | 2 | (C) | 3 | (D) | 5 |
The total number of real solutions of the equation
$$\theta = \tan ^ { - 1 } ( 2 \tan \theta ) - \frac { 1 } { 2 } \sin ^ { - 1 } \left( \frac { 6 \tan \theta } { 9 + \tan ^ { 2 } \theta } \right)$$
is\\
(Here, the inverse trigonometric functions $\sin ^ { - 1 } x$ and $\tan ^ { - 1 } x$ assume values in $\left[ - \frac { \pi } { 2 } , \frac { \pi } { 2 } \right]$ and ( $- \frac { \pi } { 2 } , \frac { \pi } { 2 }$ ), respectively.)
\begin{center}
\begin{tabular}{ | l | l | l | l | l | l | l | l | }
\hline
(A) & 1 & (B) & 2 & (C) & 3 & (D) & 5 \\
\hline
\end{tabular}
\end{center}