Point a moves in a circle with the origin as the center of the circle at a uniform speed in a counter clockwise direction. It is known that point a starts from the positive half axis of x-axis, turns the angle of θ (0 ＜ θ ＜ π) in one minute, reaches the third quadrant in two minutes, and returns to the original position in 14 minutes, then θ=______ ．

Point a moves in a circle with the origin as the center of the circle at a uniform speed in a counter clockwise direction. It is known that point a starts from the positive half axis of x-axis, turns the angle of θ (0 ＜ θ ＜ π) in one minute, reaches the third quadrant in two minutes, and returns to the original position in 14 minutes, then θ=______ ．

∵ 0 ＜ θ ＜ π, and from the meaning of the title, we can get k · 2 π + π ＜ 2 θ ＜ K · 2 π + 3 π 2 & nbsp; (K ∈ z), then there must be k = 0, so π 2 ＜ θ ＜ 3 π 4, and 14 θ = n · 2 π (n ∈ z), ∵ θ = N7 × π, ∵ π 2 ＜ N7 · π ＜ 3 π 4, 72 ＜ n ＜ 214, ∵ n = 4 or 5, so θ = 4 π 7 or 5 π 7