Determining the initial angle of a projectile's motion

Question Q8.4.3

The trajectory of a projectile in the $xz$-plane launched from the origin at an angle $\theta_0$ with speed $v_0 = 25\;\mathrm{m\,s^{-1}}$ is $$ z = x\tan\theta_0 - \frac{g}{2v_0^2\cos\theta_0}x^2. $$ If the projectile passes through the point $(5, 15)$, use Brent's method to determine the possible values of $\theta_0$.


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