Answer
$$cot^2θ-3cotθ-cotθ+3=0 $$
⇒$$cotθ(cotθ-3)-(cotθ-3)=0$$
⇒$$(cotθ-3)(cotθ-1)=0$$
⇒$$cotθ=3,1 but θ \epsilon 0<θ<π/4$$
$$∴ cotθ=3 at θ \epsilon π/6$$
$$Now, sinθ+cosθ at θ =π/6,$$
$$= sin(π/6)+cos(π/6)$$
$$= 1/2 +\sqrt{3}/2 $$
Hence the answer (C) is $$\frac{√3+1}{2}$$