by putting $\displaystyle t = tan\frac{\theta}{2}$, find the general solution of the equation

$\displaystyle 3cos\theta + 4sin\theta = 3 - tan\frac{\theta}{2}$

OK i've worked it out to

$\displaystyle t(t-3)(t-3)$

$\displaystyle \therefore t=0, t=3$

but not sure what to do from here.

I also know the general solution for tan is $\displaystyle \theta=\pi n + \alpha$