Im having a little trouble answering these problems.
Note: Q represents the symbol that looks like a zero with a line across. (Not sure what its called.
1.) 1 - 2 sin(Q) = sin(Q) - sqrt(3)
2.) 2 (sin^2)(Q) = 1 - sin (Q)
It's $\displaystyle \theta$ and it's pronounced "theta." We can stick with Q's though.
$\displaystyle 1 - 2sin(Q) = sin(Q) - \sqrt{3}$
$\displaystyle -3sin(Q) = -1 - \sqrt{3}$
$\displaystyle sin(Q) = \frac{1}{3} + \frac{\sqrt{3}}{3}$
This has no "nice" solution. So
$\displaystyle Q \approx 1.14494~rad$
-Dan