#Help
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Should be π/6, not π/3.
How?
Well, let's see.
1/sin(x) - cot(x) = (1 - cos(x))/sin(x) = 2sin(x/2)^2/(2sin(x/2)cos(x/2)) = tan(x/2)
So, we get tan(x/2 + π/12).
Ah, so their answer is incorrect.