If cot3θ = sin45°.cos45°+cos60°, then θ is ______________.

Question : If cot3θ = sin45°.cos45°+cos60°, then θ is ______________.

Doubt by Sanya

Solution : 
cot3θ = sin45°.cos45°+cos60°
cot3θ = (1/√2).(1/√2)+(1/2)
cot3θ = (1/2)+(1/2)
cot3θ = 1
cot3θ = cot45°
3θ = 45°
θ = 45°/3
θ = 15°