I was just merrily some maths, when I came up with this problem.

I don't know LATEX or any of that fancy stuff, so I'll just put it in paint.

To solve it, instead of finding the inverse function, just plug in -3 to the equation as g(x), and you get the solution, which is pi.

Well, this is all and well, right?

HOWEVER, Wolfram Alpha and my handy dandy TI-89 disagree.

Plugging the equation into Wolfram Alpha, I get not 1 point, pi, but also 3 other random points which seemingly are not supposed to exist but still do.

2-x+5cosx+pi+3=0 - Wolfram|Alpha
This is a problem, since the problem was specifically supposed to be solved without a calculator.

How would one achieve such calculations without the aid of a calculator?