Logs and Trig Exam Question Help

Been doing loads of past papers for my C2 exam next week, and both of these questions I got parts of the question wrong.



For the first one I got:

$4(1-Cos^2\theta)=3+Cos^2\theta-1[br]4Cos^2\theta + Cos^2\theta-1=0$

And I factorised using the quadratic formula to get:
$\theta= 67, 293, 130, 230$

But this is wrong...



For the second one I got n=2.71 through the use of simultaneous equations. I then substituted in n to find a value for a. I got 8.99 which is way out of the mark scheme's tolerance.

Any help will be appreciated. I can post exactly what I did if it will help, just let me know.

Thanks,
Sora

I can't read my own writing xD Thank you!

Any help on the logs?