You are not Euclid, you kid !
Find arccot(1)+arccot(2)+arccot(3) in radians.
Assume that you are a very intelligent fifth grader. You don't know anything about trigonometry but just know the definition of arccot. Solve the question now.
The answer is 1.57.
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1 solution
Obviously, we can solve this by trigonometry, but I'll show how to solve it as a fifth grader who knows the definition of arccot.
We can say that A=arccot1 or 45 (can be easily found by fifth grader by seeing the figure), B=arccot2, C=arccot3 Now we have to find A+B+C=45+B+C
Make three more squares above this diagram and do some construction.
We can easily say that angles LRZ and RTV are equal to B. So TRV is 90-B, making TRL 90.
We see that TR=RL, and TRL is an isosceles triangle, making RLT equal to 45.
Now we can see 45+B+C=90
So answer is π / 2
Note : All angles are in degrees in the solution. Most of the angles have been found by similarity and not by trigonometry.
This solution may also be considered as a conjecture which has been proved later.