JEE Main 2014 · 9 Apr · Shift 1, Mathematics question 88

With $s=\sin\alpha$:
$$2s^3-7s^2+7s-2=(s-1)(2s-1)(s-2)=0.$$

• $s=2$ is impossible.
• $s=1$ gives $\alpha=\frac\pi2$.
• $s=\frac12$ gives $\alpha=\frac\pi6,\frac{5\pi}6$.

So there are 3 values.