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It is more complicated than I thought...
You can call Wolfram|Alpha from inside Mathematica, and that can show steps for some functions.
With a plot like this you can make guesses about possible nontrivial real solutions: With[{b = 1, r = 2 Pi}, ContourPlot3D[{0 == Sin[y] - b x, 0 == Sin[z] - b y, 0 == Sin[x] - b z}, {x, -r, r}, {y, -r, r}, {z, -r, r}]]
You could do it with `Minimize`: data = RandomReal[{0, 1}, {10, 3}]; dist[{x_, y_, z_}] = RegionDistance[Sphere[{a, b, c}, r], {x, y, z}]; Minimize[{Total@Map[dist, data], r > 0}, {a, b, c, r}]
This may be a start: PolarPlot[ Abs[1/(4 Pi) + (5/16 Pi) (1 - 3 Cos[2 t]) + 9/(256 Pi) (9 - 20 Cos[2 t] + 35 Cos[4 t])], {t, 0, 2 Pi}] /. Line -> Polygon
Maybe something like this? NIntegrate[1, Element[{x, y, z}, DiscretizeGraphics@ExampleData[{"Geometry3D", "Beethoven"}]]]
I don't know what you are trying to achieve, but it may have something to do with this: {1635, 3270, 6541, 13082, 26163, 52326} /. n_Integer :> Style[Last@IntegerDigits[n], Hue[n/10]]
Saving the notebook and reopening it should give the last used values. Paste snapshot should give a `DynamicModule` with the list of current control values. I don't know of a direct, easy way to reload them, though.
Here is a way: Probability[x > 8, Distributed[x, NormalDistribution[75/10, 25/1000]]] N[%, 5]
It seems to me that your equation for `theta2''[t]` is singular when t=0 and `theta1[0] == theta2[0] == 0`.