How to get the theta in this projectile equation? The equation for the Parabolic Trajectory is
$$y = x\tan{\theta}- \frac {gx^2}{2V_0^2\cos^2{\theta}}$$
It will be easy to get any variables if there's an angle, but how I can solve if the missing one is the angle? What will be the formula to get the angle? In quadratic way and identity.
Like for example:
$$12.5 = 6.7\tan{\theta} - \frac{(9.81)(6.7)^2}{(2)(24)^2\cos^2{\theta}}$$
$\theta = ?$
Any Help is appreciated!

Note that due to the Pythagorean Trigonometric Identity : $1 + \tan^2{\theta} = \sec^2{\theta}$,
$$\begin{align}12.5 &= 6.7\tan{\theta} - \frac{(9.81)(6.7)^2}{(2)(24)^2\cos^2\theta}\\
&= 6.7\tan{\theta} - \frac{(9.81)(6.7)^2}{(2)(24)^2}\sec^2\theta \\
&= 6.7\tan{\theta} - \frac{(9.81)(6.7)^2}{(2)(24)^2}(1 + \tan^2\theta)
\end{align}$$
This reduces (after rearranging the terms) into merely a quadratic equation in $\tan{\theta}$. Solve for $\tan{\theta}$, then for $\theta$.
