Find the number of values of in such that for

MATHEMATICS · Subjective · A Level · Mathematics · Trigonometry · Trigonometry

Problem

Find the number of values of

\theta

\left(-\frac{\pi}{2},\frac{\pi}{2}\right)

such that

\theta\ne\frac{n\pi}{5}

for

n=0,\pm1,\pm2

, and both

\tan\theta=\cot5\theta

and

\sin2\theta=\cos4\theta

hold.