Trigonometry · Superchallenge problem

When the sun's angle of elevation is $\theta$, a vertical pole on level ground casts a shadow $3$ times as long as the shadow it casts when the sun's angle of elevation is $2\theta$ (with $0^\circ<2\theta<90^\circ$). The two shadows differ in length by $20$ m. Find the exact height of the pole in metres.