Explanation

14sin²θ + 10cos²θ = 11 gives 14sin²θ + 10(1 − sin²θ) = 11, so 4sin²θ = 1 and sin θ = 1/2 (θ acute). Hence θ = 30°, and tan θ + cot θ = 1/√3 + √3 = 4/√3. This is option (a).