So I'm trying to find the horizontal and vertical tangents to a polar curve, and what it comes down to is solving the following equations:

4cos(4x)sin(x) + sin(4x)cos(x) = 0

and

4cos(4x)cos(x) - sin(4x)sin(x) = 0

I'm fairly lost; I keep messing around with the equations, but it doesn't seem to get any simpler. Anything I do to it ends up being equally complex. Any suggestions?