trig help

Given: csc^2(x) + cot(x) = 7

csc^2(x) = cot^2(x) + 1

cot^2(x) + 1 + cot(x) = 7
cot^2(x) + cot(x) - 6 = 0

Let cot(x) = a
a^2 + a - 6 = 0
(a + 3)(a - 2) = 0
a = -3
a = 2

but a = cot(x)

cot(x) = -3
x = 341.57deg

cot(x) = 2
x = 26.57deg


Steub