We graph the two functions: y=sin(2x)-1 in black and tan(x) in red and note the intersections on the interval `[0,2pi]` :

The intersections (from a graphing utility) are approximately :

`x~~2.0687813` and `x~~5.210374`

We graph the two functions: y=sin(2x)-1 in black and tan(x) in red and note the intersections on the interval `[0,2pi]` :

The intersections (from a graphing utility) are approximately :

`x~~2.0687813` and `x~~5.210374`