(1)
sinθ+cosθ= -a/25 (1)
sinθcosθ=(a-7)/25 (2)
from (1)
1+2sinθcosθ = a^2/625
1+2(a-7)/25=a^2/625
a^2-50a-275 =0
(a-55)(a+5)=0
a=-5 or 55 (rejected)
(2)
when a=-5
25x^2-5x-12=0
(5x-4)(5x+3)=0
x= 4/5 or -3/5
tanθ =(4/5)/(-3/5) or (-3/5)/(4/5)
= -4/3 or -3/4