Morning!
When I ran your code, I got a time of about 6.55 seconds. The largest driver of run time are the round() function calls in the middle of your triple nested for loop.
If you take advantage of vectorized computations & logic operations, you can greatly reduce your run time (and number of lines!) by at least an order of magnitude. This can be accomplished by using the ndgrid function to generatethe combinations of t1, t2 & t3 that your triple-nested for loops would have provided.
You might want to consider the following refactoring. This produced a run time of about 0.70 (factor of 9.4x faster than your original code):
tic
range_t1 = (0:1:180)./57.2958;
range_t2 = (0:1:180)./57.2958;
range_t3 = (-90:1:90)./57.2958;
[t1, t2, t3] = ndgrid(range_t1, range_t2, range_t3);
x = round(140.*sin(t3).*sin(t2).*cos(t1) - 140.*cos(t3).*cos(t1).*cos(t2) - 180.*sin(t2).*cos(t1), 2);
y = round(119.6 + 140.*sin(t3).*sin(t1).*sin(t2) - 140.*cos(t3).*sin(t1).*cos(t2) - 180.*sin(t2).*sin(t1), 2);
z = round(-71.77 - 140.*sin(t3).*cos(t2) - 140.*cos(t3).*sin(t2) + 180.*cos(t2) + 117, 2);
logicInd = (x == 0) & (y == 0) & (z == 0);
a1 = t1(logicInd);
a2 = t2(logicInd);
a3 = t3(logicInd);
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