5sin 2x = 2cos 2x.
Divide both sides by cos.
5tan2x = 2.
2x = ArcTan (2/5)
2x = 21.8, 201.8, 381.8, 561.8. (It's 2x so you double the interval.)
x = 10.9, 100.9, 190.9, 208.9
Caution: I've been doing physics, stats and FP2 all morning so the values might be wrong, but the method should work.