Consider the shaded region bounded by $sin x$, $cos x$, and $tan x$:

We can define this as an `ImplicitRegion`

by:

```
(ScriptCapitalR) =
ImplicitRegion((0 < x < 1) (And) (y < Cos(x)) (And)
(y < Tan(x)) (And) (y > Sin(x)),
{x, y})
```

However, `RegionPlot((ScriptCapitalR))`

fails to yield a figure after 15 minutes (v 11.3, MacOS).

However if I’m “smart” and put the bounds as $0<x< pi/4$ I *do* get a plot.

Moreover, its area,

```
RegionMeasure((ScriptCapitalR))
```

does not give an analytic solution (even after `RootReduce`

, `Simplify`

, etc.) even though an analytic form exists.

(One *can* get a numerical value through `N@RegionMeasure((ScriptCapitalR))`

, but I seek the *analytic* solution.)

I’ve tried various forms based on `RegionIntersection()`

and such, without success.

Of course I can use traditional calculus through `Integrate`

and finding intersection points, but I’d like to compute the area more directly.

How can I 1) plot the region and (more importantly) 2) compute the analytic area?