3cosa+4sina can take the value of +/-5, which should be -5 in the third quadrant, so-5-4-a =+/-kloc-0/7, and the solution is a =-26/8; Synthetically, four values of a=- 16, -26, 8 and 18 are obtained.
The reference answers are-16, 18. Take only the first quadrant point.