@Carl Love I am sorry. I want to obtain x= pi/6+k*pi and x= -pi/6+k*pi.

@Thomas Richard Thank you very much.

@tomleslie Please see your code. 

http://www.artofproblemsolving.com/community/c3t243f3h621768s1_mathcounts_triangles

I have some problems:

Problem 1: In how many ways can one choose three diffenret positive integers less than or equal to 100 such that their sum is an event number?

Problem 2: Find the number of all 3-digit positive integers written with 1, 2, 3, 4, 5, 6 such that each number is divisible 3 and none of them are repeated.

How can I use your code?

@Kitonum Thank you very much.

@Kitonum Thank you very much.

@Kitonum I added x1*y1 + x2*y2 + x3*y3<>0 (the triangles non right) and x1*x2+y1*y2+z1*z2<>0  and x1*x2*y1*y2*z1*z2<>0 (six numbers x1, y1, z1, x2, y2, z2 are different from 0). How to get nine numbers x1, y1, z1, x2, y2, z2 are difference?
I tried
and x1*x2+y1*y2+z1*z2<>0  and x1*x2*y1*y2*z1*z2<>0 and x1<>y1 and x1<>z1 and y1<>z1 and x2<>y2 and x2<>z2 and y2<>z2  and igcd(x1,y1,z1)=1 and igcd(x2,y2,z2)=1

@Kitonum Thank you very much.

@Kitonum I got 

Warning, solve may be ignoring assumptions on the input variables and the out put is {a = 5/13, b = 7/13}

I want to get real solutions depending on a real parameter m.

@Markiyan Hirnyk I haven't got an answer.

@Carl Love Another request is intersection of tangents has integer coordinates. Note that, in your code, in PLK, there are some tangents repeat many times. 

@Carl Love Thank you very much.

@Kitonum 

@Markiyan Hirnyk I used my hand to substituted w into z. How can I do it without by hand?