How can I solve these two equations to find theta? I am doing a projectile motion questions and I have to solve these simultaneous equations:
$$\frac{-5t^{2}+30t\sin\theta }{30t\cos\theta }=\frac{1}{\sqrt3}$$
$$\frac{-10t+30\sin\theta }{30\cos\theta }=-\sqrt3$$
I solved them but the solution is long and tedious and I got theta = $-60^\circ$ which is wrong.
Thank you in advance!

Subtracting the second from the first equation gives
$$\frac{t}{6\cos\theta} = \frac{4}{3}\sqrt{3}$$
or
$$t=8\sqrt{3}\cos\theta.$$
Plugging this back into the first equation gives
$$ \frac{-4\sqrt{3}\cos\theta+3\sin\theta}{3\cos\theta} = \frac{1}{3}\sqrt{3}$$
or
$$3\sin\theta = 5\sqrt{3}\cos\theta.$$
Thus finally we have
$$\tan\theta = \frac{5}{3}\sqrt{3}$$
and
$$ \frac{25}{3} = \tan(\theta)^2 = \cos(\theta)^{-2}-1,$$
thus
$$ t = \pm\frac{12}{7}\sqrt{7}.$$
