I came across a word problem that I can't seem to puzzle through. I know the answer to it, but I can not seem to find out how to get to it.

"A block is set in motion hanging from a spring and oscillates about it's resting position x=0, according to the function $\displaystyle x=\sqrt{3}sin2t+cos2t$. For what values of t is the block at it's resting position x=0."

This is how I've worked it so far.

$\displaystyle 0=\sqrt{3}sin2t+cos2t$

$\displaystyle -cos2t=\sqrt{3}sin2t$

$\displaystyle -\frac{cos2t}{sin2t}=\sqrt{3}$

$\displaystyle -cot2t=\sqrt{3}$

$\displaystyle tan2t=\frac{1}{\sqrt{3}}$

$\displaystyle 2t=tan^-^1(\frac{1}{\sqrt{3}})$

$\displaystyle 2t = 30\deg$

$\displaystyle t = 15\deg$

This answer, unfortunately, is not correct. I know that the correct answer is 75 degrees, but I have no clue how to get to that answer.

Any help would be appreciated. I've been puzzling over this question for a while now.