[SOLVED] Quadratic Trigonometric Equations

Hi there, I'm new. (Hi) I'd really like to get a tutor's help with this, but I can't wait until Monday, so I hope you won't mind my asking.

Anyway, this has got me really stumped. The book is no help; all the examples are much less complicated. I'll just post two examples I'm having trouble with for now.

In this section I'm supposed to find all values for $\displaystyle \theta$:

1.) $\displaystyle cos (2\theta) + 6 sin^2\theta = 4$

What I tried to do was to move the 4 to the left side, convert to all sine values, and plug the values into the quadratic formula. I ended up with $\displaystyle \frac {\sqrt {15}}{5}$ and $\displaystyle -\frac {\sqrt {15}}{5}$ . This is probably wrong, even though I'm fairly sure I didn't make any algebraic errors (I probably just chose the wrong process).

2.) $\displaystyle tan\theta = 2 sin\theta$

I tried converting to all sin and cos values. I think my mistake was to try to divide both sides by $\displaystyle sin\theta$ after that, since dividing by a variable is a no-no. I ended up with $\displaystyle cos\theta = \frac {1}{2}$ , which resulted in two correct answers (as special angles), but there are supposed to be four.

Any help is greatly appreciated and will result in my abject adoration, and cake.